167:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento numérico y variacional :@0.603816:0.043660:0.930949:0.043660:0.930949:0.024915:0.603816:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.1 Suma de los  primeros términos de una progresión aritmética:@0.073089:0.136836:0.589858:0.136836:0.589858:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 n:@0.195423:0.136836:0.208842:0.136836:0.208842:0.119889:0.195423:0.119889:0.000000:0.000000
La suma de los   primeros términos de una progresión aritmética es::@0.073089:0.164198:0.568113:0.164198:0.568113:0.147764:0.073089:0.147764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.184177:0.164198:0.193675:0.164198:0.193675:0.147792:0.184177:0.147792:0.000000
S:@0.247810:0.184418:0.255873:0.184418:0.255873:0.168012:0.247810:0.168012:0.000000
n:@0.255825:0.187588:0.261362:0.187588:0.261362:0.178023:0.255825:0.178023:0.000000
 =   +   + ... + :@0.261324:0.184415:0.376170:0.184415:0.376170:0.167982:0.261324:0.167982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.280117:0.184415:0.289431:0.184415:0.289431:0.168009:0.280117:0.168009:0.000000
0:@0.289455:0.187588:0.294692:0.187588:0.294692:0.178007:0.289455:0.178007:0.000000
u:@0.313768:0.184415:0.323082:0.184415:0.323082:0.168009:0.313768:0.168009:0.000000
1:@0.323105:0.187588:0.328342:0.187588:0.328342:0.178007:0.323105:0.178007:0.000000
u:@0.376133:0.184415:0.385447:0.184415:0.385447:0.168009:0.376133:0.168009:0.000000
n:@0.385465:0.187588:0.391003:0.187588:0.391003:0.178023:0.385465:0.178023:0.000000
–2:@0.390960:0.187588:0.401573:0.187588:0.401573:0.178007:0.390960:0.178007:0.000000:0.000000
 + :@0.401580:0.184415:0.420650:0.184415:0.420650:0.167982:0.401580:0.167982:0.000000:0.000000:0.000000
u:@0.420650:0.184415:0.429964:0.184415:0.429964:0.168009:0.420650:0.168009:0.000000
n:@0.429988:0.187588:0.435525:0.187588:0.435525:0.178023:0.429988:0.178023:0.000000
–1:@0.435482:0.187588:0.446095:0.187588:0.446095:0.178007:0.435482:0.178007:0.000000:0.000000
,     = 1, 2, ...:@0.446639:0.184415:0.531663:0.184415:0.531663:0.167982:0.446639:0.167982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.461973:0.184415:0.471471:0.184415:0.471471:0.168009:0.461973:0.168009:0.000000
Observemos los siguientes resultados::@0.073064:0.215355:0.349313:0.215355:0.349313:0.198922:0.073064:0.198922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.073064:0.239139:0.082378:0.239139:0.082378:0.222733:0.073064:0.222733:0.000000
0:@0.082429:0.242313:0.087666:0.242313:0.087666:0.232732:0.082429:0.232732:0.000000
 + :@0.087672:0.239141:0.106742:0.239141:0.106742:0.222707:0.087672:0.222707:0.000000:0.000000:0.000000
u:@0.106742:0.239141:0.116056:0.239141:0.116056:0.222735:0.106742:0.222735:0.000000
n:@0.116079:0.242313:0.121616:0.242313:0.121616:0.232748:0.116079:0.232748:0.000000
–1:@0.121627:0.242313:0.132241:0.242313:0.132241:0.232732:0.121627:0.232732:0.000000:0.000000
 =   +   + (  – 1)  = 2  + (  – 1):@0.132247:0.239141:0.380805:0.239141:0.380805:0.222707:0.132247:0.222707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.151317:0.239141:0.160631:0.239141:0.160631:0.222735:0.151317:0.222735:0.000000
0:@0.160654:0.242313:0.165891:0.242313:0.165891:0.232732:0.160654:0.232732:0.000000
u:@0.184967:0.239141:0.194281:0.239141:0.194281:0.222735:0.184967:0.222735:0.000000
0:@0.194304:0.242313:0.199541:0.242313:0.199541:0.232732:0.194304:0.232732:0.000000
n:@0.223495:0.239141:0.232993:0.239141:0.232993:0.222735:0.223495:0.222735:0.000000
d:@0.264193:0.239141:0.273452:0.239141:0.273452:0.222735:0.264193:0.222735:0.000000
u:@0.301523:0.239141:0.310837:0.239141:0.310837:0.222735:0.301523:0.222735:0.000000
0:@0.310896:0.242313:0.316133:0.242313:0.316133:0.232732:0.310896:0.232732:0.000000
n:@0.340088:0.239141:0.349586:0.239141:0.349586:0.222735:0.340088:0.222735:0.000000
d,:@0.380787:0.239141:0.393064:0.239141:0.393064:0.222735:0.380787:0.222735:0.000000:0.000000
u:@0.073073:0.262925:0.082387:0.262925:0.082387:0.246519:0.073073:0.246519:0.000000
1:@0.082429:0.266103:0.087666:0.266103:0.087666:0.256522:0.082429:0.256522:0.000000
+:@0.091722:0.262931:0.102693:0.262931:0.102693:0.246497:0.091722:0.246497:0.000000
u:@0.106742:0.262931:0.116056:0.262931:0.116056:0.246525:0.106742:0.246525:0.000000
n:@0.116079:0.266103:0.121616:0.266103:0.121616:0.256539:0.116079:0.256539:0.000000
–2:@0.121627:0.266103:0.132241:0.266103:0.132241:0.256522:0.121627:0.256522:0.000000:0.000000
 =   +   +   + (  – 2)  = 2  + (  – 1):@0.132247:0.262931:0.409156:0.262931:0.409156:0.246497:0.132247:0.246497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.151317:0.262931:0.160631:0.262931:0.160631:0.246525:0.151317:0.246525:0.000000
0:@0.160654:0.266103:0.165891:0.266103:0.165891:0.256522:0.160654:0.256522:0.000000
d:@0.184967:0.262931:0.194226:0.262931:0.194226:0.246525:0.184967:0.246525:0.000000
u:@0.213314:0.262931:0.222628:0.262931:0.222628:0.246525:0.213314:0.246525:0.000000
0:@0.222655:0.266103:0.227892:0.266103:0.227892:0.256522:0.222655:0.256522:0.000000
n:@0.251847:0.262931:0.261345:0.262931:0.261345:0.246525:0.251847:0.246525:0.000000
d:@0.292546:0.262931:0.301804:0.262931:0.301804:0.246525:0.292546:0.246525:0.000000
u:@0.329876:0.262931:0.339190:0.262931:0.339190:0.246525:0.329876:0.246525:0.000000
0:@0.339248:0.266103:0.344485:0.266103:0.344485:0.256522:0.339248:0.256522:0.000000
n:@0.368439:0.262931:0.377937:0.262931:0.377937:0.246525:0.368439:0.246525:0.000000
d,:@0.409137:0.262931:0.421415:0.262931:0.421415:0.246525:0.409137:0.246525:0.000000:0.000000
∙:@0.073076:0.287297:0.082280:0.287297:0.082280:0.269643:0.073076:0.269643:0.000000
u:@0.073076:0.306935:0.082390:0.306935:0.082390:0.290529:0.073076:0.290529:0.000000
n:@0.082429:0.310108:0.087966:0.310108:0.087966:0.300544:0.082429:0.300544:0.000000
–1:@0.087977:0.310108:0.098590:0.310108:0.098590:0.300527:0.087977:0.300527:0.000000:0.000000
+:@0.102647:0.306936:0.113617:0.306936:0.113617:0.290502:0.102647:0.290502:0.000000
u:@0.117667:0.306936:0.126981:0.306936:0.126981:0.290530:0.117667:0.290530:0.000000
0:@0.127004:0.310108:0.132241:0.310108:0.132241:0.300527:0.127004:0.300527:0.000000
 =   + (  – 1)  +   :@0.132247:0.306936:0.277527:0.306936:0.277527:0.290502:0.132247:0.290502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.151317:0.306936:0.160631:0.306936:0.160631:0.290530:0.151317:0.290530:0.000000
0:@0.160654:0.310108:0.165891:0.310108:0.165891:0.300527:0.160654:0.300527:0.000000
n:@0.189845:0.306936:0.199343:0.306936:0.199343:0.290530:0.189845:0.290530:0.000000
d:@0.230543:0.306936:0.239802:0.306936:0.239802:0.290530:0.230543:0.290530:0.000000
u = 2u:@0.258890:0.306936:0.309703:0.306936:0.309703:0.290530:0.258890:0.290530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.268251:0.310108:0.273488:0.310108:0.273488:0.300527:0.268251:0.300527:0.000000
0:@0.309743:0.310108:0.314980:0.310108:0.314980:0.300527:0.309743:0.300527:0.000000
 + (  – 1):@0.314986:0.306936:0.379650:0.306936:0.379650:0.290502:0.314986:0.290502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.338934:0.306936:0.348432:0.306936:0.348432:0.290530:0.338934:0.290530:0.000000
d,:@0.379632:0.306936:0.391910:0.306936:0.391910:0.290530:0.379632:0.290530:0.000000:0.000000
y de manera general, para 0 ≤   ≤   – 1 se tiene::@0.073078:0.341440:0.417919:0.341440:0.417919:0.325006:0.073078:0.325006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.292603:0.341440:0.300168:0.341440:0.300168:0.325034:0.292603:0.325034:0.000000
n:@0.318888:0.341440:0.328386:0.341440:0.328386:0.325034:0.318888:0.325034:0.000000
u:@0.073059:0.361660:0.082373:0.361660:0.082373:0.345254:0.073059:0.345254:0.000000
n:@0.082429:0.364835:0.087966:0.364835:0.087966:0.355270:0.082429:0.355270:0.000000
–1–:@0.087977:0.364835:0.103967:0.364835:0.103967:0.355254:0.087977:0.355254:0.000000:0.000000:0.000000
k:@0.103967:0.364835:0.108377:0.364835:0.108377:0.355270:0.103967:0.355270:0.000000
 +   =   + (  – 1 –  )  +   + :@0.108395:0.361662:0.326437:0.361662:0.326437:0.345229:0.108395:0.345229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.127465:0.361662:0.136779:0.361662:0.136779:0.345256:0.127465:0.345256:0.000000
k:@0.136802:0.364835:0.141212:0.364835:0.141212:0.355270:0.136802:0.355270:0.000000
u:@0.160298:0.361662:0.169612:0.361662:0.169612:0.345256:0.160298:0.345256:0.000000
0:@0.169634:0.364835:0.174871:0.364835:0.174871:0.355254:0.169634:0.355254:0.000000
n:@0.198826:0.361662:0.208324:0.361662:0.208324:0.345256:0.198826:0.345256:0.000000
k d:@0.251931:0.361662:0.273670:0.361662:0.273670:0.345256:0.251931:0.345256:0.000000:0.000000:0.000000
u:@0.292758:0.361662:0.302072:0.361662:0.302072:0.345256:0.292758:0.345256:0.000000
0:@0.302122:0.364835:0.307359:0.364835:0.307359:0.355254:0.302122:0.355254:0.000000
kd = 2u:@0.326437:0.361662:0.378647:0.361662:0.378647:0.345256:0.326437:0.345256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.378707:0.364835:0.383944:0.364835:0.383944:0.355254:0.378707:0.355254:0.000000
 + (  – 1):@0.383949:0.361662:0.448614:0.361662:0.448614:0.345229:0.383949:0.345229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.407897:0.361662:0.417395:0.361662:0.417395:0.345256:0.407897:0.345256:0.000000
d.:@0.448596:0.361662:0.460873:0.361662:0.460873:0.345256:0.448596:0.345256:0.000000:0.000000
Luego, de la definición de   y de los resultados precedentes, tenemos::@0.073069:0.396166:0.584068:0.396173:0.584068:0.379739:0.073069:0.379733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.263548:0.396166:0.271610:0.396166:0.271610:0.379760:0.263548:0.379760:0.000000
n:@0.271555:0.399345:0.277092:0.399345:0.277092:0.389780:0.271555:0.389780:0.000000
2  = 2(  +   + ... + :@0.073083:0.427113:0.224032:0.427109:0.224032:0.410675:0.073083:0.410679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.081991:0.427109:0.090053:0.427109:0.090053:0.410703:0.081991:0.410703:0.000000
n:@0.089987:0.430281:0.095524:0.430281:0.095524:0.420717:0.089987:0.420717:0.000000
u:@0.127975:0.427109:0.137289:0.427109:0.137289:0.410703:0.127975:0.410703:0.000000
0:@0.137316:0.430281:0.142552:0.430281:0.142552:0.420700:0.137316:0.420700:0.000000
u:@0.161630:0.427109:0.170944:0.427109:0.170944:0.410703:0.161630:0.410703:0.000000
1:@0.170967:0.430281:0.176204:0.430281:0.176204:0.420700:0.170967:0.420700:0.000000
u:@0.223995:0.427109:0.233309:0.427109:0.233309:0.410703:0.223995:0.410703:0.000000
n:@0.233328:0.430281:0.238865:0.430281:0.238865:0.420717:0.233328:0.420717:0.000000
–2:@0.238822:0.430281:0.249436:0.430281:0.249436:0.420700:0.238822:0.420700:0.000000:0.000000
 + :@0.249443:0.427109:0.268512:0.427109:0.268512:0.410675:0.249443:0.410675:0.000000:0.000000:0.000000
u:@0.268512:0.427109:0.277827:0.427109:0.277827:0.410703:0.268512:0.410703:0.000000
n:@0.277850:0.430281:0.283387:0.430281:0.283387:0.420717:0.277850:0.420717:0.000000
–1:@0.283345:0.430281:0.293958:0.430281:0.293958:0.420700:0.283345:0.420700:0.000000:0.000000
):@0.293965:0.427109:0.298843:0.427109:0.298843:0.410675:0.293965:0.410675:0.000000
= (  +   + ... + :@0.073096:0.456260:0.188784:0.456260:0.188784:0.439826:0.073096:0.439826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.092737:0.456260:0.102051:0.456260:0.102051:0.439854:0.092737:0.439854:0.000000
0:@0.102067:0.459432:0.107303:0.459432:0.107303:0.449851:0.102067:0.449851:0.000000
u:@0.126380:0.456260:0.135694:0.456260:0.135694:0.439854:0.126380:0.439854:0.000000
1:@0.135718:0.459432:0.140954:0.459432:0.140954:0.449851:0.135718:0.449851:0.000000
u:@0.188747:0.456260:0.198061:0.456260:0.198061:0.439854:0.188747:0.439854:0.000000
n:@0.198078:0.459432:0.203615:0.459432:0.203615:0.449867:0.198078:0.449867:0.000000
–2:@0.203573:0.459432:0.214186:0.459432:0.214186:0.449851:0.203573:0.449851:0.000000:0.000000
 + :@0.214193:0.456260:0.233263:0.456260:0.233263:0.439826:0.214193:0.439826:0.000000:0.000000:0.000000
u:@0.233263:0.456260:0.242577:0.456260:0.242577:0.439854:0.233263:0.439854:0.000000
n:@0.242600:0.459432:0.248137:0.459432:0.248137:0.449867:0.242600:0.449867:0.000000
–1:@0.248095:0.459432:0.258708:0.459432:0.258708:0.449851:0.248095:0.449851:0.000000:0.000000
) + (  +   + ... + :@0.258715:0.456260:0.383526:0.456260:0.383526:0.439826:0.258715:0.439826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.287467:0.456260:0.296781:0.456260:0.296781:0.439854:0.287467:0.439854:0.000000
0:@0.296809:0.459432:0.302046:0.459432:0.302046:0.449851:0.296809:0.449851:0.000000
u:@0.321122:0.456260:0.330436:0.456260:0.330436:0.439854:0.321122:0.439854:0.000000
1:@0.330460:0.459432:0.335696:0.459432:0.335696:0.449851:0.330460:0.449851:0.000000
u:@0.383489:0.456260:0.392803:0.456260:0.392803:0.439854:0.383489:0.439854:0.000000
n:@0.392820:0.459432:0.398357:0.459432:0.398357:0.449867:0.392820:0.449867:0.000000
–2:@0.398315:0.459432:0.408928:0.459432:0.408928:0.449851:0.398315:0.449851:0.000000:0.000000
 + :@0.408935:0.456260:0.428005:0.456260:0.428005:0.439826:0.408935:0.439826:0.000000:0.000000:0.000000
u:@0.428005:0.456260:0.437319:0.456260:0.437319:0.439854:0.428005:0.439854:0.000000
n:@0.437342:0.459432:0.442880:0.459432:0.442880:0.449867:0.437342:0.449867:0.000000
–1:@0.442837:0.459432:0.453450:0.459432:0.453450:0.449851:0.442837:0.449851:0.000000:0.000000
):@0.453457:0.456260:0.458335:0.456260:0.458335:0.439826:0.453457:0.439826:0.000000
= (  + :@0.073089:0.485411:0.126380:0.485410:0.126380:0.468976:0.073089:0.468977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.092730:0.485411:0.102044:0.485411:0.102044:0.469005:0.092730:0.469005:0.000000
0:@0.102067:0.488582:0.107304:0.488582:0.107304:0.479001:0.102067:0.479001:0.000000
u:@0.126380:0.485410:0.135694:0.485410:0.135694:0.469003:0.126380:0.469003:0.000000
n:@0.135718:0.488582:0.141255:0.488582:0.141255:0.479017:0.135718:0.479017:0.000000
–1:@0.141212:0.488582:0.151825:0.488582:0.151825:0.479001:0.141212:0.479001:0.000000:0.000000
) + (  + :@0.151832:0.485410:0.214332:0.485410:0.214332:0.468976:0.151832:0.468976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.180676:0.485410:0.189990:0.485410:0.189990:0.469003:0.180676:0.469003:0.000000
1:@0.190019:0.488582:0.195256:0.488582:0.195256:0.479001:0.190019:0.479001:0.000000
u:@0.214332:0.485410:0.223646:0.485410:0.223646:0.469003:0.214332:0.469003:0.000000
n:@0.223669:0.488582:0.229206:0.488582:0.229206:0.479017:0.223669:0.479017:0.000000
–2:@0.229164:0.488582:0.239777:0.488582:0.239777:0.479001:0.229164:0.479001:0.000000:0.000000
) + ... + (:@0.239784:0.485410:0.297398:0.485410:0.297398:0.468976:0.239784:0.468976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.297251:0.485410:0.306565:0.485410:0.306565:0.469003:0.297251:0.469003:0.000000
n:@0.306587:0.488582:0.312124:0.488582:0.312124:0.479017:0.306587:0.479017:0.000000
–1:@0.312082:0.488582:0.322695:0.488582:0.322695:0.479001:0.312082:0.479001:0.000000:0.000000
+  ):@0.322702:0.485410:0.357189:0.485410:0.357189:0.468976:0.322702:0.468976:0.000000:0.000000:0.000000:0.000000
u:@0.337722:0.485410:0.347036:0.485410:0.347036:0.469003:0.337722:0.469003:0.000000
0:@0.347066:0.488582:0.352303:0.488582:0.352303:0.479001:0.347066:0.479001:0.000000
= 2  + ( – 1)  + 2  + ( – 1)  + ... + 2  + ( – 1):@0.073091:0.514560:0.435687:0.514559:0.435687:0.498125:0.073091:0.498127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.096836:0.514560:0.106150:0.514560:0.106150:0.498154:0.096836:0.498154:0.000000
0:@0.106172:0.517732:0.111408:0.517732:0.111408:0.508151:0.106172:0.508151:0.000000
n :@0.135363:0.514559:0.148193:0.514559:0.148193:0.498153:0.135363:0.498153:0.000000:0.000000
d:@0.175362:0.514559:0.184621:0.514559:0.184621:0.498153:0.175362:0.498153:0.000000
u:@0.212600:0.514559:0.221914:0.514559:0.221914:0.498153:0.212600:0.498153:0.000000
0:@0.221971:0.517732:0.227207:0.517732:0.227207:0.508151:0.221971:0.508151:0.000000
n :@0.251161:0.514559:0.263991:0.514559:0.263991:0.498153:0.251161:0.498153:0.000000:0.000000
d:@0.291160:0.514559:0.300419:0.514559:0.300419:0.498153:0.291160:0.498153:0.000000
u:@0.357113:0.514559:0.366427:0.514559:0.366427:0.498153:0.357113:0.498153:0.000000
0:@0.366479:0.517732:0.371716:0.517732:0.371716:0.508151:0.366479:0.508151:0.000000
n :@0.395670:0.514559:0.408500:0.514559:0.408500:0.498153:0.395670:0.498153:0.000000:0.000000
d:@0.435669:0.514559:0.444928:0.514559:0.444928:0.498153:0.435669:0.498153:0.000000
=  [2  + ( – 1) ], de donde:@0.073083:0.543710:0.282267:0.543709:0.282267:0.527275:0.073083:0.527276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n u:@0.087919:0.543710:0.120537:0.543710:0.120537:0.527304:0.087919:0.527304:0.000000:0.000000:0.000000
0:@0.120584:0.546881:0.125821:0.546881:0.125821:0.537300:0.120584:0.537300:0.000000
n :@0.149775:0.543709:0.162605:0.543709:0.162605:0.527303:0.149775:0.527303:0.000000:0.000000
d:@0.189774:0.543709:0.199033:0.543709:0.199033:0.527303:0.189774:0.527303:0.000000
S:@0.073072:0.574177:0.081135:0.574177:0.081135:0.557771:0.073072:0.557771:0.000000
n:@0.081085:0.577354:0.086622:0.577354:0.086622:0.567789:0.081085:0.567789:0.000000
 =    (2  + ( – 1) ).:@0.086583:0.574181:0.242603:0.574181:0.242603:0.557747:0.086583:0.557747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.107998:0.567605:0.116981:0.567605:0.116981:0.551171:0.107998:0.551171:0.000000
2:@0.107998:0.583997:0.116981:0.583997:0.116981:0.567563:0.107998:0.567563:0.000000
n u:@0.123479:0.574179:0.156004:0.574179:0.156004:0.557773:0.123479:0.557773:0.000000:0.000000:0.000000
0:@0.156037:0.577354:0.161274:0.577354:0.161274:0.567772:0.156037:0.567772:0.000000
n :@0.185228:0.574181:0.198058:0.574181:0.198058:0.557775:0.185228:0.557775:0.000000:0.000000
d:@0.225227:0.574181:0.234486:0.574181:0.234486:0.557775:0.225227:0.557775:0.000000
Por otro lado, :@0.073073:0.612263:0.174887:0.612263:0.174887:0.595829:0.073073:0.595829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.175255:0.612263:0.184569:0.612263:0.184569:0.595857:0.175255:0.595857:0.000000
n:@0.184651:0.615438:0.190188:0.615438:0.190188:0.605873:0.184651:0.605873:0.000000
–1:@0.190167:0.615438:0.200802:0.615438:0.200802:0.605857:0.190167:0.605857:0.000000:0.000000
 =  + (  – 1) , entonces, 2  + ( – 1)  =   +   + ( – 1)  =   +  . :@0.200839:0.612266:0.710372:0.612266:0.710372:0.595832:0.200839:0.595832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.220572:0.612266:0.229886:0.612266:0.229886:0.595860:0.220572:0.595860:0.000000
0:@0.229946:0.615438:0.235183:0.615438:0.235183:0.605857:0.229946:0.605857:0.000000
n:@0.257000:0.612266:0.266498:0.612266:0.266498:0.595860:0.257000:0.595860:0.000000
d:@0.298213:0.612266:0.307472:0.612266:0.307472:0.595860:0.298213:0.595860:0.000000
u:@0.399048:0.612266:0.408362:0.612266:0.408362:0.595860:0.399048:0.595860:0.000000
0:@0.408446:0.615438:0.413683:0.615438:0.413683:0.605857:0.408446:0.605857:0.000000
n :@0.438657:0.612266:0.451524:0.612266:0.451524:0.595860:0.438657:0.595860:0.000000:0.000000
d:@0.479650:0.612266:0.488909:0.612266:0.488909:0.595860:0.479650:0.595860:0.000000
u:@0.508973:0.612266:0.518287:0.612266:0.518287:0.595860:0.508973:0.595860:0.000000
0:@0.518352:0.615438:0.523589:0.615438:0.523589:0.605857:0.518352:0.605857:0.000000
u:@0.543631:0.612266:0.552945:0.612266:0.552945:0.595860:0.543631:0.595860:0.000000
0:@0.553005:0.615438:0.558242:0.615438:0.558242:0.605857:0.553005:0.605857:0.000000
n :@0.583216:0.612266:0.596083:0.612266:0.596083:0.595860:0.583216:0.595860:0.000000:0.000000
d:@0.624209:0.612266:0.633468:0.612266:0.633468:0.595860:0.624209:0.595860:0.000000
u:@0.653532:0.612266:0.662846:0.612266:0.662846:0.595860:0.653532:0.595860:0.000000
0:@0.662911:0.615438:0.668148:0.615438:0.668148:0.605857:0.662911:0.605857:0.000000
u:@0.688189:0.612266:0.697504:0.612266:0.697504:0.595860:0.688189:0.595860:0.000000
n:@0.697564:0.615438:0.703101:0.615438:0.703101:0.605873:0.697564:0.605873:0.000000
Luego,:@0.073094:0.628908:0.122026:0.628908:0.122026:0.612474:0.073094:0.612474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.197619:0.652234:0.205682:0.652234:0.205682:0.635828:0.197619:0.635828:0.000000
n:@0.205607:0.655405:0.211144:0.655405:0.211144:0.645840:0.205607:0.645840:0.000000
 =    (2  + ( – 1) ) =    (  + :@0.211105:0.652233:0.449170:0.652233:0.449170:0.635799:0.211105:0.635799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.232520:0.645657:0.241502:0.645657:0.241502:0.629223:0.232520:0.629223:0.000000
2:@0.232520:0.662049:0.241502:0.662049:0.241502:0.645615:0.232520:0.645615:0.000000
n u:@0.248000:0.652230:0.280526:0.652230:0.280526:0.635824:0.248000:0.635824:0.000000:0.000000:0.000000
0:@0.280559:0.655405:0.285796:0.655405:0.285796:0.645824:0.280559:0.645824:0.000000
n :@0.309750:0.652233:0.322580:0.652233:0.322580:0.635826:0.309750:0.635826:0.000000:0.000000
d:@0.349749:0.652233:0.359008:0.652233:0.359008:0.635826:0.349749:0.635826:0.000000
1:@0.385626:0.645657:0.394609:0.645657:0.394609:0.629223:0.385626:0.629223:0.000000
2:@0.385626:0.662049:0.394609:0.662049:0.394609:0.645615:0.385626:0.645615:0.000000
n u:@0.401199:0.652230:0.424834:0.652230:0.424834:0.635824:0.401199:0.635824:0.000000:0.000000:0.000000
0:@0.424855:0.655405:0.430092:0.655405:0.430092:0.645824:0.424855:0.645824:0.000000
u:@0.449170:0.652233:0.458484:0.652233:0.458484:0.635826:0.449170:0.635826:0.000000
n:@0.458505:0.655405:0.464043:0.655405:0.464043:0.645840:0.458505:0.645840:0.000000
–1:@0.464054:0.655405:0.474667:0.655405:0.474667:0.645824:0.464054:0.645824:0.000000:0.000000
) =   :@0.474674:0.652233:0.512169:0.652233:0.512169:0.635799:0.474674:0.635799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.498622:0.652233:0.508120:0.652233:0.508120:0.635826:0.498622:0.635826:0.000000
u:@0.516135:0.645657:0.525449:0.645657:0.525449:0.629250:0.516135:0.629250:0.000000
0:@0.525384:0.646307:0.530621:0.646307:0.530621:0.636726:0.525384:0.636726:0.000000
 + :@0.530573:0.645657:0.549459:0.645657:0.549459:0.629223:0.530573:0.629223:0.000000:0.000000:0.000000
u:@0.549367:0.645657:0.558681:0.645657:0.558681:0.629250:0.549367:0.629250:0.000000
n:@0.558612:0.646307:0.564150:0.646307:0.564150:0.636743:0.558612:0.636743:0.000000
–1:@0.564107:0.646307:0.574667:0.646307:0.574667:0.636726:0.564107:0.636726:0.000000:0.000000
2:@0.540910:0.662046:0.549892:0.662046:0.549892:0.645612:0.540910:0.645612:0.000000
.:@0.578608:0.652228:0.581811:0.652228:0.581811:0.635794:0.578608:0.635794:0.000000
Es decir que la suma de los   primeros términos  ,  , ..., :@0.073071:0.689006:0.482552:0.689012:0.482552:0.672578:0.073071:0.672572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.271575:0.689006:0.281073:0.689006:0.281073:0.672600:0.271575:0.672600:0.000000
u u:@0.422606:0.689006:0.453638:0.689012:0.453638:0.672606:0.422606:0.672600:0.000000:0.000000:0.000000
0:@0.431974:0.692185:0.437211:0.692185:0.437211:0.682604:0.431974:0.682604:0.000000
1:@0.453654:0.692185:0.458891:0.692185:0.458891:0.682604:0.453654:0.682604:0.000000
u:@0.482460:0.689012:0.491774:0.689012:0.491774:0.672606:0.482460:0.672606:0.000000
n:@0.491799:0.692185:0.497337:0.692185:0.497337:0.682620:0.491799:0.682620:0.000000
–1:@0.497347:0.692185:0.507961:0.692185:0.507961:0.682604:0.497347:0.682604:0.000000:0.000000
 de la progresión aritmética :@0.507967:0.689012:0.710508:0.689012:0.710508:0.672578:0.507967:0.672578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) es igual a   veces la media aritmética de   y :@0.073096:0.707928:0.426852:0.707923:0.426852:0.691490:0.073096:0.691495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.077992:0.707928:0.087306:0.707928:0.087306:0.691522:0.077992:0.691522:0.000000
n:@0.087318:0.711096:0.092855:0.711096:0.092855:0.701531:0.087318:0.701531:0.000000
n:@0.172960:0.707923:0.182459:0.707923:0.182459:0.691517:0.172960:0.691517:0.000000
u:@0.396240:0.707923:0.405554:0.707923:0.405554:0.691517:0.396240:0.691517:0.000000
0:@0.405593:0.711096:0.410830:0.711096:0.410830:0.701515:0.405593:0.701515:0.000000
u:@0.426760:0.707923:0.436074:0.707923:0.436074:0.691517:0.426760:0.691517:0.000000
n:@0.436097:0.711096:0.441635:0.711096:0.441635:0.701531:0.436097:0.701531:0.000000
–1:@0.441645:0.711096:0.452259:0.711096:0.452259:0.701515:0.441645:0.701515:0.000000:0.000000
.:@0.452265:0.707923:0.455468:0.707923:0.455468:0.691490:0.452265:0.691490:0.000000
Particularmente, si   = 1 y   = 0, se tiene:   = 1 + 2 + ... +   =    ( + 1),  :@0.073094:0.741332:0.640844:0.741336:0.640844:0.724902:0.073094:0.724898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.215346:0.741332:0.224604:0.741332:0.224604:0.724926:0.215346:0.724926:0.000000
u:@0.273163:0.741332:0.282477:0.741332:0.282477:0.724926:0.273163:0.724926:0.000000
0:@0.282663:0.744511:0.287899:0.744511:0.287899:0.734930:0.282663:0.734930:0.000000
S:@0.393687:0.741338:0.401749:0.741338:0.401749:0.724932:0.393687:0.724932:0.000000
n:@0.401828:0.744511:0.407365:0.744511:0.407365:0.734946:0.401828:0.734946:0.000000
n:@0.520028:0.741338:0.529526:0.741338:0.529526:0.724932:0.520028:0.724932:0.000000
1:@0.553373:0.734762:0.562356:0.734762:0.562356:0.718328:0.553373:0.718328:0.000000
2:@0.553373:0.751154:0.562356:0.751154:0.562356:0.734721:0.553373:0.734721:0.000000
n n :@0.570105:0.741336:0.597541:0.741336:0.597541:0.724930:0.570105:0.724930:0.000000:0.000000:0.000000:0.000000
∀:@0.641894:0.741918:0.654171:0.741918:0.654171:0.724264:0.641894:0.724264:0.000000
n:@0.654282:0.741336:0.663780:0.741336:0.663780:0.724930:0.654282:0.724930:0.000000
    , :@0.663853:0.741336:0.710360:0.741338:0.710360:0.724904:0.663853:0.724902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.668925:0.741737:0.683562:0.741737:0.683562:0.724885:0.668925:0.724885:0.000000
ℕ:@0.688695:0.741921:0.703016:0.741921:0.703016:0.724266:0.688695:0.724266:0.000000
fórmula que se conocecomo suma de los n primeros números naturales.:@0.073083:0.764027:0.600411:0.764032:0.600411:0.747598:0.073083:0.747593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.239767:0.767204:0.242117:0.767204:0.242117:0.757623:0.239767:0.757623:0.000000
Ejercicio 3:@0.073091:0.804457:0.149494:0.804457:0.149494:0.787788:0.073091:0.787788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Halla la suma de los 10 primeros términos de la progresión aritmética siguiente:                  :@0.073091:0.828241:0.710641:0.828241:0.710641:0.811808:0.073091:0.811808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20, 17, 14, ... :@0.073091:0.844883:0.161300:0.844883:0.161300:0.828449:0.073091:0.828449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ponemos   = 20,   = 17, entonces,   =   +  , con lo que   =   –   = 17 – 20 = –3.:@0.073091:0.872245:0.686258:0.872258:0.686258:0.855824:0.073091:0.855811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.145560:0.872245:0.154819:0.872245:0.154819:0.855839:0.145560:0.855839:0.000000
0:@0.154841:0.875430:0.160078:0.875430:0.160078:0.865849:0.154841:0.865849:0.000000
a:@0.203747:0.872258:0.213006:0.872258:0.213006:0.855852:0.203747:0.855852:0.000000
1:@0.213036:0.875430:0.218273:0.875430:0.218273:0.865849:0.213036:0.865849:0.000000
a:@0.336198:0.872258:0.345456:0.872258:0.345456:0.855852:0.336198:0.855852:0.000000
1:@0.345490:0.875430:0.350727:0.875430:0.350727:0.865849:0.345490:0.865849:0.000000
a:@0.369526:0.872258:0.378785:0.872258:0.378785:0.855852:0.369526:0.855852:0.000000
0:@0.378809:0.875430:0.384046:0.875430:0.384046:0.865849:0.378809:0.865849:0.000000
d:@0.402845:0.872258:0.412104:0.872258:0.412104:0.855852:0.402845:0.855852:0.000000
d:@0.500643:0.872258:0.509902:0.872258:0.509902:0.855852:0.500643:0.855852:0.000000
a:@0.528622:0.872258:0.537881:0.872258:0.537881:0.855852:0.528622:0.855852:0.000000
1:@0.537914:0.875430:0.543151:0.875430:0.543151:0.865849:0.537914:0.865849:0.000000
a:@0.560185:0.872258:0.569444:0.872258:0.569444:0.855852:0.560185:0.855852:0.000000
0:@0.569468:0.875430:0.574705:0.875430:0.574705:0.865849:0.569468:0.865849:0.000000
Luego, para   = 10 se tiene:    =   (2  + ( – 1) ) = :@0.073094:0.902726:0.459433:0.902729:0.459433:0.886296:0.073094:0.886292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.161799:0.902726:0.171297:0.902726:0.171297:0.886320:0.161799:0.886320:0.000000
S:@0.279219:0.902726:0.287281:0.902726:0.287281:0.886320:0.279219:0.886320:0.000000
10:@0.287231:0.905902:0.297104:0.905902:0.297104:0.896337:0.287231:0.896337:0.000000:0.000000
n:@0.318227:0.896153:0.327725:0.896153:0.327725:0.879747:0.318227:0.879747:0.000000
2:@0.318485:0.912546:0.327468:0.912546:0.327468:0.896112:0.318485:0.896112:0.000000
u:@0.347660:0.902727:0.356974:0.902727:0.356974:0.886321:0.347660:0.886321:0.000000
0:@0.356999:0.905902:0.362236:0.905902:0.362236:0.896321:0.356999:0.896321:0.000000
n :@0.386190:0.902729:0.399020:0.902729:0.399020:0.886323:0.386190:0.886323:0.000000:0.000000
d:@0.426189:0.902729:0.435448:0.902729:0.435448:0.886323:0.426189:0.886323:0.000000
10:@0.459988:0.896153:0.477880:0.896153:0.477880:0.879720:0.459988:0.879720:0.000000:0.000000
2:@0.464443:0.912546:0.473425:0.912546:0.473425:0.896112:0.464443:0.896112:0.000000
 (2 × 20 + 9 ×(–3)) = 65.:@0.478432:0.902727:0.649605:0.902727:0.649605:0.886293:0.478432:0.886293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La suma de los 10 primeros términos es 65.:@0.073086:0.933667:0.384360:0.933667:0.384360:0.917233:0.073086:0.917233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740294:0.150262:0.848854:0.150262:0.848854:0.133315:0.740294:0.133315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.166904:0.837769:0.166904:0.837769:0.149957:0.740294:0.149957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otras formas de escribir :@0.744288:0.186502:0.903787:0.186502:0.903787:0.171562:0.744288:0.171562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los términos de una :@0.744288:0.201631:0.878648:0.201631:0.878648:0.186691:0.744288:0.186691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
progresión aritmética son::@0.744288:0.216760:0.916153:0.216760:0.916153:0.201820:0.744288:0.201820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Diferencia.:@0.744288:0.239037:0.813488:0.239037:0.813488:0.224097:0.744288:0.224097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• La diferencia :@0.744288:0.254165:0.850048:0.254165:0.850048:0.239225:0.744288:0.239225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.849911:0.254165:0.858328:0.254165:0.858328:0.239250:0.849911:0.239250:0.000000
puede ser positiva, :@0.763263:0.269294:0.890423:0.269294:0.890423:0.254354:0.763263:0.254354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
negativa o nula. Si es :@0.763263:0.284423:0.904229:0.284423:0.904229:0.269483:0.763263:0.269483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
positiva la progresión :@0.763263:0.299552:0.908026:0.299552:0.908026:0.284612:0.763263:0.284612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es creciente, y :@0.763263:0.314681:0.859328:0.314681:0.859328:0.299741:0.763263:0.299741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decreciente cuando :@0.763263:0.329810:0.899080:0.329810:0.899080:0.314870:0.763263:0.314870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d :@0.898907:0.329810:0.910337:0.329810:0.910337:0.314895:0.898907:0.314895:0.000000:0.000000
es negativa.:@0.763263:0.344939:0.841075:0.344939:0.841075:0.329999:0.763263:0.329999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• Se calcula restando dos:@0.744288:0.367215:0.917536:0.367215:0.917536:0.352275:0.744288:0.352275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos consecutivos.:@0.763263:0.382344:0.915079:0.382344:0.915079:0.367404:0.763263:0.367404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Notación y término :@0.744286:0.404621:0.875985:0.404621:0.875985:0.389681:0.744286:0.389681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.744286:0.419750:0.752921:0.419750:0.752921:0.404835:0.744286:0.404835:0.000000
-ésimo.:@0.752854:0.419750:0.800835:0.419750:0.800835:0.404810:0.752854:0.404810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.744286:0.434879:0.755649:0.434879:0.755649:0.419964:0.744286:0.419964:0.000000:0.000000
= primer término;:@0.755599:0.434879:0.872573:0.434879:0.872573:0.419939:0.755599:0.419939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.744286:0.450008:0.752704:0.450008:0.752704:0.435093:0.744286:0.435093:0.000000
 = diferencia:@0.752637:0.450008:0.834368:0.450008:0.834368:0.435068:0.752637:0.435068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Término n-ésimo::@0.744286:0.465137:0.859512:0.465137:0.859512:0.450197:0.744286:0.450197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.744286:0.480266:0.752754:0.480266:0.752754:0.465351:0.744286:0.465351:0.000000
n:@0.752695:0.483150:0.757924:0.483150:0.757924:0.474440:0.752695:0.474440:0.000000
 =   + (  – 1)   o:@0.757881:0.480266:0.868659:0.480266:0.868659:0.465326:0.757881:0.465326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.774966:0.480266:0.783383:0.480266:0.783383:0.465351:0.774966:0.465351:0.000000
n:@0.804753:0.480266:0.813387:0.480266:0.813387:0.465351:0.804753:0.465351:0.000000
d :@0.841249:0.480266:0.852611:0.480266:0.852611:0.465351:0.841249:0.465351:0.000000:0.000000
l  a:@0.744276:0.495395:0.772523:0.495395:0.772523:0.480480:0.744276:0.480480:0.000000:0.000000:0.000000:0.000000
=   + (  – 1):@0.750619:0.495395:0.830489:0.495395:0.830489:0.480455:0.750619:0.480455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.793892:0.495395:0.802527:0.495395:0.802527:0.480480:0.793892:0.480480:0.000000
d:@0.830389:0.495395:0.838806:0.495395:0.838806:0.480480:0.830389:0.480480:0.000000
Suma de los n primeros :@0.744260:0.517672:0.903494:0.517672:0.903494:0.502732:0.744260:0.502732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos.:@0.744260:0.532801:0.805988:0.532801:0.805988:0.517861:0.744260:0.517861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• Se calcula con la:@0.744288:0.547929:0.871725:0.547929:0.871725:0.532989:0.744288:0.532989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguiente fórmula::@0.763263:0.563058:0.882003:0.563058:0.882003:0.548118:0.763263:0.548118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que es equivalente a :@0.763263:0.623421:0.903218:0.623421:0.903218:0.608481:0.763263:0.608481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000