171:@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
3.1 Suma de los primeros términos de una progresión geométrica:@0.073089:0.136836:0.586436:0.136836:0.586436:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.073089:0.165211:0.113338:0.165211:0.113338:0.148777:0.073089:0.148777:0.000000:0.000000:0.000000:0.000000:0.000000
a, d:@0.113272:0.165211:0.138637:0.165211:0.138637:0.148804:0.113272:0.148804:0.000000:0.000000:0.000000:0.000000
     no nulos y      , la progresión geométrica ( ) definida como   = :@0.138784:0.165211:0.678835:0.165208:0.678835:0.148774:0.138784:0.148777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.142747:0.165606:0.157384:0.165606:0.157384:0.148755:0.142747:0.148755:0.000000
ℝ:@0.161448:0.165790:0.174738:0.165790:0.174738:0.148136:0.161448:0.148136:0.000000
n:@0.259521:0.165208:0.269020:0.165208:0.269020:0.148802:0.259521:0.148802:0.000000
∈:@0.273128:0.165606:0.287764:0.165606:0.287764:0.148755:0.273128:0.148755:0.000000
ℕ:@0.291828:0.165790:0.306149:0.165790:0.306149:0.148136:0.291828:0.148136:0.000000
u:@0.508941:0.165208:0.518255:0.165208:0.518255:0.148802:0.508941:0.148802:0.000000
n:@0.518381:0.168380:0.523918:0.168380:0.523918:0.158816:0.518381:0.158816:0.000000
u:@0.644702:0.165208:0.654016:0.165208:0.654016:0.148802:0.644702:0.148802:0.000000
n:@0.654141:0.168380:0.659678:0.168380:0.659678:0.158816:0.654141:0.158816:0.000000
ad:@0.678780:0.165208:0.697408:0.165208:0.697408:0.148802:0.678780:0.148802:0.000000:0.000000
n:@0.697532:0.159144:0.703069:0.159144:0.703069:0.149579:0.697532:0.149579:0.000000
,   :@0.703138:0.165208:0.710372:0.165208:0.710372:0.148774:0.703138:0.148774:0.000000:0.000000:0.000000:0.000000
∀:@0.073094:0.183445:0.085372:0.183445:0.085372:0.165790:0.073094:0.165790:0.000000
n:@0.085464:0.182862:0.094962:0.182862:0.094962:0.166456:0.085464:0.166456:0.000000
    . Consideramos la suma de los primeros   + 1 términos de esta progresión::@0.095073:0.182862:0.684762:0.182858:0.684762:0.166425:0.095073:0.166428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.099209:0.183257:0.113845:0.183257:0.113845:0.166405:0.099209:0.166405:0.000000
ℕ:@0.118074:0.183441:0.132395:0.183441:0.132395:0.165787:0.118074:0.165787:0.000000
n:@0.430445:0.182858:0.439944:0.182858:0.439944:0.166452:0.430445:0.166452:0.000000
S:@0.318180:0.210220:0.326242:0.210220:0.326242:0.193814:0.318180:0.193814:0.000000
n:@0.326169:0.213394:0.331706:0.213394:0.331706:0.203829:0.326169:0.203829:0.000000
 =   +   + ... + :@0.331668:0.210222:0.446516:0.210222:0.446516:0.193788:0.331668:0.193788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.350462:0.210222:0.359776:0.210222:0.359776:0.193816:0.350462:0.193816:0.000000
0:@0.359799:0.213394:0.365036:0.213394:0.365036:0.203813:0.359799:0.203813:0.000000
u:@0.384113:0.210222:0.393427:0.210222:0.393427:0.193816:0.384113:0.193816:0.000000
1:@0.393449:0.213394:0.398686:0.213394:0.398686:0.203813:0.393449:0.203813:0.000000
u:@0.446479:0.210222:0.455793:0.210222:0.455793:0.193816:0.446479:0.193816:0.000000
n:@0.455719:0.213394:0.461257:0.213394:0.461257:0.203829:0.455719:0.203829:0.000000
=   +   + :@0.240841:0.235313:0.320931:0.235313:0.320931:0.218879:0.240841:0.218879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.255678:0.235313:0.264936:0.235313:0.264936:0.218907:0.255678:0.218907:0.000000
ad:@0.283657:0.235313:0.302101:0.235313:0.302101:0.218907:0.283657:0.218907:0.000000:0.000000
ad:@0.320839:0.235313:0.339283:0.235313:0.339283:0.218907:0.320839:0.218907:0.000000:0.000000
2:@0.339228:0.229249:0.344465:0.229249:0.344465:0.219668:0.339228:0.219668:0.000000
 + ... + :@0.344417:0.235313:0.391503:0.235313:0.391503:0.218879:0.344417:0.218879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad:@0.391374:0.235313:0.409818:0.235313:0.409818:0.218907:0.391374:0.218907:0.000000:0.000000
n:@0.409751:0.229249:0.415289:0.229249:0.415289:0.219684:0.409751:0.219684:0.000000
–1:@0.415246:0.229249:0.425805:0.229249:0.425805:0.219668:0.415246:0.219668:0.000000:0.000000
 + :@0.425759:0.235313:0.444645:0.235313:0.444645:0.218879:0.425759:0.218879:0.000000:0.000000:0.000000
ad:@0.444553:0.235313:0.462997:0.235313:0.462997:0.218907:0.444553:0.218907:0.000000:0.000000
n:@0.462937:0.229249:0.468474:0.229249:0.468474:0.219684:0.462937:0.219684:0.000000
 = :@0.468435:0.235313:0.487321:0.235313:0.487321:0.218879:0.468435:0.218879:0.000000:0.000000:0.000000
a :@0.487229:0.235313:0.499728:0.235313:0.499728:0.218907:0.487229:0.218907:0.000000:0.000000
∑:@0.500998:0.240432:0.515606:0.240432:0.515606:0.213540:0.500998:0.213540:0.000000
n:@0.506187:0.220907:0.511724:0.220907:0.511724:0.211342:0.506187:0.211342:0.000000
k:@0.501175:0.245623:0.505586:0.245623:0.505586:0.236058:0.501175:0.236058:0.000000
=0:@0.505543:0.245623:0.517133:0.245623:0.517133:0.236042:0.505543:0.236042:0.000000:0.000000
 d:@0.518573:0.235313:0.531072:0.235313:0.531072:0.218907:0.518573:0.218907:0.000000:0.000000
k:@0.531013:0.229249:0.535424:0.229249:0.535424:0.219684:0.531013:0.219684:0.000000
.:@0.535384:0.235313:0.538587:0.235313:0.538587:0.218879:0.535384:0.218879:0.000000
Si multiplicamos a   por  , tenemos:  :@0.073086:0.266253:0.347332:0.266250:0.347332:0.249817:0.073086:0.249819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.208895:0.266253:0.216957:0.266253:0.216957:0.249847:0.208895:0.249847:0.000000
n:@0.216890:0.269423:0.222428:0.269423:0.222428:0.259858:0.216890:0.259858:0.000000
d:@0.255430:0.266250:0.264689:0.266250:0.264689:0.249844:0.255430:0.249844:0.000000
dS:@0.347172:0.266250:0.364419:0.266250:0.364419:0.249844:0.347172:0.249844:0.000000:0.000000
n:@0.364377:0.269423:0.369915:0.269423:0.369915:0.259858:0.364377:0.259858:0.000000
 =   + :@0.369876:0.266250:0.425945:0.266250:0.425945:0.249817:0.369876:0.249817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad:@0.388670:0.266250:0.407114:0.266250:0.407114:0.249844:0.388670:0.249844:0.000000:0.000000
ad:@0.425853:0.266250:0.444297:0.266250:0.444297:0.249844:0.425853:0.249844:0.000000:0.000000
2:@0.444228:0.260187:0.449465:0.260187:0.449465:0.250606:0.444228:0.250606:0.000000
 + :@0.449419:0.266250:0.468305:0.266250:0.468305:0.249817:0.449419:0.249817:0.000000:0.000000:0.000000
ad:@0.468213:0.266250:0.486657:0.266250:0.486657:0.249844:0.468213:0.249844:0.000000:0.000000
3:@0.486595:0.260187:0.491832:0.260187:0.491832:0.250606:0.486595:0.250606:0.000000
 + ... + :@0.491786:0.266250:0.538872:0.266250:0.538872:0.249817:0.491786:0.249817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad:@0.538743:0.266250:0.557187:0.266250:0.557187:0.249844:0.538743:0.249844:0.000000:0.000000
n:@0.557120:0.260187:0.562657:0.260187:0.562657:0.250622:0.557120:0.250622:0.000000
 + :@0.562619:0.266250:0.581504:0.266250:0.581504:0.249817:0.562619:0.249817:0.000000:0.000000:0.000000
ad:@0.581412:0.266250:0.599856:0.266250:0.599856:0.249844:0.581412:0.249844:0.000000:0.000000
n:@0.599795:0.260187:0.605332:0.260187:0.605332:0.250622:0.599795:0.250622:0.000000
+1:@0.605289:0.260187:0.616879:0.260187:0.616879:0.250606:0.605289:0.250606:0.000000:0.000000
.:@0.616833:0.266250:0.620036:0.266250:0.620036:0.249817:0.616833:0.249817:0.000000
Luego, :@0.073083:0.293612:0.125972:0.293612:0.125972:0.277179:0.073083:0.277179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dS:@0.125856:0.293612:0.143104:0.293612:0.143104:0.277206:0.125856:0.277206:0.000000:0.000000
n:@0.143057:0.296786:0.148594:0.296786:0.148594:0.287221:0.143057:0.287221:0.000000
 –   = :@0.148556:0.293614:0.197959:0.293614:0.197959:0.277180:0.148556:0.277180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.165582:0.293614:0.173645:0.293614:0.173645:0.277208:0.165582:0.277208:0.000000
n:@0.173575:0.296786:0.179112:0.296786:0.179112:0.287221:0.173575:0.287221:0.000000
ad:@0.197867:0.293614:0.216311:0.293614:0.216311:0.277208:0.197867:0.277208:0.000000:0.000000
n:@0.216249:0.287550:0.221787:0.287550:0.221787:0.277985:0.216249:0.277985:0.000000
+1:@0.221744:0.287550:0.233334:0.287550:0.233334:0.277969:0.221744:0.277969:0.000000:0.000000
 –   =  (:@0.233286:0.293614:0.292355:0.293614:0.292355:0.277180:0.233286:0.277180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.250313:0.293614:0.259572:0.293614:0.259572:0.277208:0.250313:0.277208:0.000000
a d:@0.278292:0.293614:0.301540:0.293614:0.301540:0.277208:0.278292:0.277208:0.000000:0.000000:0.000000
n:@0.301477:0.287550:0.307014:0.287550:0.307014:0.277985:0.301477:0.277985:0.000000
+1:@0.306971:0.287550:0.318561:0.287550:0.318561:0.277969:0.306971:0.277969:0.000000:0.000000
 – 1), o lo que es lo mismo, :@0.318513:0.293614:0.514239:0.293614:0.514239:0.277180:0.318513:0.277180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  – 1)  =  (:@0.314151:0.320976:0.405206:0.320977:0.405206:0.304543:0.314151:0.304542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.318955:0.320976:0.328214:0.320976:0.328214:0.304570:0.318955:0.304570:0.000000
S:@0.358862:0.320976:0.366924:0.320976:0.366924:0.304570:0.358862:0.304570:0.000000
n:@0.366851:0.324149:0.372388:0.324149:0.372388:0.314585:0.366851:0.314585:0.000000
a d:@0.391143:0.320977:0.414392:0.320977:0.414392:0.304571:0.391143:0.304571:0.000000:0.000000:0.000000
n:@0.414323:0.314913:0.419860:0.314913:0.419860:0.305348:0.414323:0.305348:0.000000
+1:@0.419818:0.314913:0.431407:0.314913:0.431407:0.305332:0.419818:0.305332:0.000000:0.000000
 – 1).:@0.431360:0.320977:0.465321:0.320977:0.465321:0.304543:0.431360:0.304543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   = 1, entonces ( ) es la sucesión constante  , en cuyo caso:@0.073081:0.348339:0.523933:0.348340:0.523933:0.331906:0.073081:0.331905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.089261:0.348339:0.098520:0.348339:0.098520:0.331933:0.089261:0.331933:0.000000
u:@0.209442:0.348339:0.218756:0.348339:0.218756:0.331933:0.209442:0.331933:0.000000
n:@0.218791:0.351512:0.224329:0.351512:0.224329:0.341948:0.218791:0.341948:0.000000
a:@0.412650:0.348340:0.421908:0.348340:0.421908:0.331934:0.412650:0.331934:0.000000
S:@0.073091:0.375702:0.081153:0.375702:0.081153:0.359296:0.073091:0.359296:0.000000
n:@0.081085:0.378876:0.086622:0.378876:0.086622:0.369311:0.081085:0.369311:0.000000
 = (  + 1) . Si   ≠ 1, entonces :@0.086583:0.375703:0.300062:0.375703:0.300062:0.359269:0.086583:0.359269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.110163:0.375703:0.119661:0.375703:0.119661:0.359297:0.110163:0.359297:0.000000
a:@0.152093:0.375703:0.161352:0.375703:0.161352:0.359297:0.152093:0.359297:0.000000
d:@0.184527:0.375703:0.193786:0.375703:0.193786:0.359297:0.184527:0.359297:0.000000
S:@0.248198:0.408834:0.256260:0.408834:0.256260:0.392428:0.248198:0.392428:0.000000
n:@0.256200:0.412008:0.261737:0.412008:0.261737:0.402443:0.256200:0.402443:0.000000
 = :@0.261698:0.408836:0.280584:0.408836:0.280584:0.392402:0.261698:0.392402:0.000000:0.000000:0.000000
a  :@0.280492:0.408836:0.296230:0.408836:0.296230:0.392430:0.280492:0.392430:0.000000:0.000000:0.000000
∑:@0.297507:0.413060:0.312116:0.413060:0.312116:0.386169:0.297507:0.386169:0.000000
n:@0.302937:0.393536:0.308475:0.393536:0.308475:0.383971:0.302937:0.383971:0.000000
k:@0.297690:0.418252:0.302100:0.418252:0.302100:0.408687:0.297690:0.408687:0.000000
=0:@0.302057:0.418252:0.313647:0.418252:0.313647:0.408671:0.302057:0.408671:0.000000:0.000000
 d:@0.315083:0.408836:0.327581:0.408836:0.327581:0.392430:0.315083:0.392430:0.000000:0.000000
k:@0.327523:0.402772:0.331933:0.402772:0.331933:0.393207:0.327523:0.393207:0.000000
 =    :@0.331895:0.408836:0.367863:0.408836:0.367863:0.392402:0.331895:0.392402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.350689:0.408836:0.359948:0.408836:0.359948:0.392430:0.350689:0.392430:0.000000
d:@0.371307:0.402260:0.380566:0.402260:0.380566:0.385854:0.371307:0.385854:0.000000
n:@0.380501:0.396196:0.386038:0.396196:0.386038:0.386631:0.380501:0.386631:0.000000
+1:@0.385995:0.396196:0.397585:0.396196:0.397585:0.386615:0.385995:0.386615:0.000000:0.000000
 – 1 :@0.397537:0.402260:0.427596:0.402260:0.427596:0.385826:0.397537:0.385826:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.379829:0.418652:0.389088:0.418652:0.389088:0.402246:0.379829:0.402246:0.000000
 – 1:@0.389015:0.418652:0.415043:0.418652:0.415043:0.402218:0.389015:0.402218:0.000000:0.000000:0.000000:0.000000
  = :@0.426989:0.408833:0.449832:0.408833:0.449832:0.392399:0.426989:0.392399:0.000000:0.000000:0.000000:0.000000
a  :@0.449722:0.408833:0.465460:0.408833:0.465460:0.392427:0.449722:0.392427:0.000000:0.000000:0.000000
1 – :@0.468964:0.402260:0.494992:0.402260:0.494992:0.385826:0.468964:0.385826:0.000000:0.000000:0.000000:0.000000
d:@0.494882:0.402260:0.504140:0.402260:0.504140:0.385854:0.494882:0.385854:0.000000
n:@0.504083:0.396196:0.509621:0.396196:0.509621:0.386631:0.504083:0.386631:0.000000
+1:@0.509578:0.396196:0.521168:0.396196:0.521168:0.386615:0.509578:0.386615:0.000000:0.000000
 :@0.521167:0.402260:0.525198:0.402260:0.525198:0.385826:0.521167:0.385826:0.000000
1 – :@0.477468:0.418652:0.503496:0.418652:0.503496:0.402218:0.477468:0.402218:0.000000:0.000000:0.000000:0.000000
d:@0.503386:0.418652:0.512645:0.418652:0.512645:0.402246:0.503386:0.402246:0.000000
 .:@0.524628:0.408833:0.531199:0.408833:0.531199:0.392427:0.524628:0.392427:0.000000:0.000000
Particularmente, si   = 1, obtenemos: :@0.073061:0.443337:0.345444:0.443337:0.345444:0.426903:0.073061:0.426903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.209900:0.443337:0.219159:0.443337:0.219159:0.426931:0.209900:0.426931:0.000000
S:@0.203568:0.477370:0.211631:0.477370:0.211631:0.460964:0.203568:0.460964:0.000000
n:@0.211599:0.480545:0.217136:0.480545:0.217136:0.470980:0.211599:0.470980:0.000000
 = 1 + :@0.217098:0.477372:0.263705:0.477372:0.263705:0.460938:0.217098:0.460938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d + d:@0.263576:0.477372:0.299396:0.477372:0.299396:0.460966:0.263576:0.460966:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.299366:0.471308:0.304603:0.471308:0.304603:0.461727:0.299366:0.461727:0.000000
 + ... +   = :@0.304557:0.477372:0.385290:0.477372:0.385290:0.460938:0.304557:0.460938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.351514:0.477372:0.360773:0.477372:0.360773:0.460966:0.351514:0.460966:0.000000
n:@0.360698:0.471308:0.366450:0.471308:0.366450:0.461727:0.360698:0.461727:0.000000
∑:@0.386526:0.480703:0.401135:0.480703:0.401135:0.453811:0.386526:0.453811:0.000000
n:@0.391955:0.461178:0.397492:0.461178:0.397492:0.451614:0.391955:0.451614:0.000000
j:@0.387855:0.485895:0.389970:0.485895:0.389970:0.476330:0.387855:0.476330:0.000000
=0:@0.389927:0.485895:0.401517:0.485895:0.401517:0.476314:0.389927:0.476314:0.000000:0.000000
    =  :@0.404089:0.477372:0.447021:0.477372:0.447021:0.460938:0.404089:0.460938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.411985:0.477372:0.421244:0.477372:0.421244:0.460966:0.411985:0.460966:0.000000
j:@0.422103:0.471308:0.424217:0.471308:0.424217:0.461744:0.422103:0.461744:0.000000
d:@0.450448:0.469902:0.459707:0.469902:0.459707:0.453496:0.450448:0.453496:0.000000
n:@0.459640:0.463838:0.465177:0.463838:0.465177:0.454274:0.459640:0.454274:0.000000
+1:@0.465135:0.463838:0.476724:0.463838:0.476724:0.454258:0.465135:0.454258:0.000000:0.000000
 – 1 :@0.476677:0.469902:0.506736:0.469902:0.506736:0.453469:0.476677:0.453469:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.458969:0.486295:0.468228:0.486295:0.468228:0.469888:0.458969:0.469888:0.000000
 – 1:@0.468154:0.486295:0.494182:0.486295:0.494182:0.469861:0.468154:0.469861:0.000000:0.000000:0.000000:0.000000
  , si   ≠ 1:@0.506128:0.477377:0.572579:0.477377:0.572579:0.460944:0.506128:0.460944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.535598:0.477377:0.544857:0.477377:0.544857:0.460971:0.535598:0.460971:0.000000
.:@0.572468:0.477377:0.575800:0.477377:0.575800:0.460971:0.572468:0.460971:0.000000
Ejercicios 3:@0.073061:0.511881:0.156680:0.511881:0.156680:0.495212:0.073061:0.495212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  De una progresión geométrica ( ) se conocen los términos:@0.073089:0.535672:0.535381:0.535672:0.535381:0.519238:0.073089:0.519238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.334798:0.535672:0.344057:0.535672:0.344057:0.519266:0.334798:0.519266:0.000000
n:@0.344076:0.538844:0.349613:0.538844:0.349613:0.529279:0.344076:0.529279:0.000000
g:@0.103210:0.567929:0.112469:0.567929:0.112469:0.551523:0.103210:0.551523:0.000000
2:@0.112402:0.571104:0.117639:0.571104:0.117639:0.561523:0.112402:0.561523:0.000000
 =   , y   = :@0.117592:0.567932:0.206793:0.567932:0.206793:0.551498:0.117592:0.551498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.139007:0.559568:0.147990:0.559568:0.147990:0.543134:0.139007:0.543134:0.000000
8:@0.139007:0.575960:0.147990:0.575960:0.147990:0.559526:0.139007:0.559526:0.000000
g:@0.173521:0.567930:0.182780:0.567930:0.182780:0.551524:0.173521:0.551524:0.000000
5:@0.182716:0.571104:0.187953:0.571104:0.187953:0.561523:0.182716:0.561523:0.000000
243:@0.208721:0.560462:0.235522:0.560462:0.235522:0.544028:0.208721:0.544028:0.000000:0.000000:0.000000
64:@0.213175:0.576854:0.231067:0.576854:0.231067:0.560420:0.213175:0.560420:0.000000:0.000000
 .:@0.237454:0.567937:0.244615:0.567937:0.244615:0.551503:0.237454:0.551503:0.000000:0.000000
Obtén el término general de esta progresión, así como la suma de los   primeros :@0.103210:0.595299:0.710401:0.595299:0.710401:0.578865:0.103210:0.578865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.626308:0.595299:0.635806:0.595299:0.635806:0.578893:0.626308:0.578893:0.000000
términos.:@0.103210:0.612953:0.171111:0.612953:0.171111:0.596519:0.103210:0.596519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se ha visto que el término general de una progresión geométrica ( ) está definido :@0.103210:0.641327:0.710459:0.641317:0.710459:0.624883:0.103210:0.624893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.587984:0.641327:0.597243:0.641327:0.597243:0.624921:0.587984:0.624921:0.000000
n:@0.597261:0.644489:0.602798:0.644489:0.602798:0.634925:0.597261:0.634925:0.000000
como    = :@0.103204:0.658971:0.190031:0.658967:0.190031:0.642534:0.103204:0.642537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.155407:0.658971:0.164665:0.658971:0.164665:0.642565:0.155407:0.642565:0.000000
n:@0.164784:0.662140:0.170322:0.662140:0.170322:0.652575:0.164784:0.652575:0.000000
ad n:@0.190601:0.658967:0.232059:0.658967:0.232059:0.642561:0.190601:0.642561:0.000000:0.000000:0.000000:0.000000
n:@0.209169:0.652904:0.214707:0.652904:0.214707:0.643339:0.209169:0.643339:0.000000
,      . Con la información dada, obtenemos las constantes   y  . :@0.214720:0.658967:0.710355:0.658967:0.710355:0.642534:0.214720:0.642534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.236872:0.659366:0.251508:0.659366:0.251508:0.642514:0.236872:0.642514:0.000000
ℕ:@0.256322:0.659550:0.270643:0.659550:0.270643:0.641896:0.256322:0.641896:0.000000
a d:@0.667227:0.658967:0.703103:0.658967:0.703103:0.642561:0.667227:0.642561:0.000000:0.000000:0.000000
Tenemos el siguiente par de ecuaciones::@0.103192:0.676622:0.396672:0.676622:0.396672:0.660188:0.103192:0.660188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.103192:0.707992:0.112451:0.707992:0.112451:0.691585:0.103192:0.691585:0.000000
2:@0.112402:0.711155:0.117639:0.711155:0.117639:0.701574:0.112402:0.701574:0.000000
 =   = :@0.117592:0.707983:0.169416:0.707980:0.169416:0.691546:0.117592:0.691549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.139007:0.701407:0.147990:0.701407:0.147990:0.684973:0.139007:0.684973:0.000000
8:@0.139007:0.717799:0.147990:0.717799:0.147990:0.701365:0.139007:0.701365:0.000000
ad:@0.169324:0.707980:0.187768:0.707980:0.187768:0.691574:0.169324:0.691574:0.000000:0.000000
2:@0.187708:0.701919:0.192945:0.701919:0.192945:0.692338:0.187708:0.692338:0.000000
,     = :@0.192899:0.707983:0.241139:0.707983:0.241139:0.691549:0.192899:0.691549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.207864:0.707983:0.217123:0.707983:0.217123:0.691577:0.207864:0.691577:0.000000
5:@0.217064:0.711155:0.222301:0.711155:0.222301:0.701574:0.217064:0.701574:0.000000
243:@0.241882:0.700514:0.268683:0.700514:0.268683:0.684080:0.241882:0.684080:0.000000:0.000000:0.000000
64:@0.246337:0.716906:0.264229:0.716906:0.264229:0.700472:0.246337:0.700472:0.000000:0.000000
 = :@0.269419:0.707989:0.288305:0.707989:0.288305:0.691555:0.269419:0.691555:0.000000:0.000000:0.000000
ad:@0.288213:0.707989:0.306657:0.707989:0.306657:0.691583:0.288213:0.691583:0.000000:0.000000
5:@0.306600:0.701919:0.311837:0.701919:0.311837:0.692338:0.306600:0.692338:0.000000
.:@0.311791:0.707983:0.314994:0.707983:0.314994:0.691549:0.311791:0.691549:0.000000
De la primera ecuación se obtiene   = :@0.103219:0.740240:0.383285:0.740240:0.383285:0.723806:0.103219:0.723806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.355214:0.740240:0.364473:0.740240:0.364473:0.723834:0.355214:0.723834:0.000000
9:@0.391737:0.731879:0.400720:0.731879:0.400720:0.715445:0.391737:0.715445:0.000000
8:@0.384558:0.748271:0.393541:0.748271:0.393541:0.731837:0.384558:0.731837:0.000000
d:@0.393468:0.748271:0.402726:0.748271:0.402726:0.731865:0.393468:0.731865:0.000000
2:@0.402658:0.742205:0.407895:0.742205:0.407895:0.732624:0.402658:0.732624:0.000000
 ,  y se reemplaza en:@0.409192:0.740243:0.554142:0.740243:0.554142:0.723809:0.409192:0.723809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la segunda ecuación, :@0.103209:0.771613:0.260094:0.771613:0.260094:0.755179:0.103209:0.755179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
243:@0.260676:0.764745:0.287477:0.764745:0.287477:0.748311:0.260676:0.748311:0.000000:0.000000:0.000000
64:@0.265131:0.781137:0.283022:0.781137:0.283022:0.764704:0.265131:0.764704:0.000000:0.000000
   = :@0.288195:0.771610:0.314996:0.771610:0.314996:0.755176:0.288195:0.755176:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.323431:0.764138:0.332414:0.764138:0.332414:0.747704:0.323431:0.747704:0.000000
8:@0.316253:0.780530:0.325235:0.780530:0.325235:0.764096:0.316253:0.764096:0.000000
d:@0.325162:0.780530:0.334420:0.780530:0.334420:0.764124:0.325162:0.764124:0.000000
2:@0.334350:0.774463:0.339587:0.774463:0.339587:0.764882:0.334350:0.764882:0.000000
    =     ,:@0.340886:0.771607:0.421596:0.771607:0.421596:0.755174:0.340886:0.755174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.348783:0.771607:0.358042:0.771607:0.358042:0.755201:0.348783:0.755201:0.000000
5:@0.357980:0.765544:0.363217:0.765544:0.363217:0.755963:0.357980:0.755963:0.000000
9:@0.384584:0.764138:0.393566:0.764138:0.393566:0.747704:0.384584:0.747704:0.000000
8:@0.384584:0.780530:0.393566:0.780530:0.393566:0.764096:0.384584:0.764096:0.000000
d:@0.404003:0.771613:0.413262:0.771613:0.413262:0.755206:0.404003:0.755206:0.000000
3:@0.413204:0.765544:0.418440:0.765544:0.418440:0.755963:0.413204:0.755963:0.000000
de donde   = :@0.103205:0.803865:0.211368:0.803867:0.211368:0.787434:0.103205:0.787431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.178104:0.803865:0.187363:0.803865:0.187363:0.787459:0.178104:0.787459:0.000000
3:@0.187291:0.797804:0.192528:0.797804:0.192528:0.788223:0.187291:0.788223:0.000000
27:@0.211818:0.795504:0.229710:0.795504:0.229710:0.779070:0.211818:0.779070:0.000000:0.000000
8:@0.216273:0.811896:0.225255:0.811896:0.225255:0.795462:0.216273:0.795462:0.000000
 , y en consecuencia,   =   . Calculamos  : :@0.230170:0.803866:0.540076:0.803866:0.540076:0.787432:0.230170:0.787432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.382711:0.803866:0.391970:0.803866:0.391970:0.787460:0.382711:0.787460:0.000000
3:@0.413306:0.795504:0.422288:0.795504:0.422288:0.779070:0.413306:0.779070:0.000000
2:@0.413306:0.811896:0.422288:0.811896:0.422288:0.795462:0.413306:0.795462:0.000000
a:@0.523657:0.803866:0.532916:0.803866:0.532916:0.787460:0.523657:0.787460:0.000000
a:@0.103217:0.835236:0.112476:0.835236:0.112476:0.818830:0.103217:0.818830:0.000000
 = :@0.112402:0.835236:0.131288:0.835236:0.131288:0.818802:0.112402:0.818802:0.000000:0.000000:0.000000
9:@0.139745:0.827762:0.148728:0.827762:0.148728:0.811328:0.139745:0.811328:0.000000
8:@0.132567:0.844155:0.141549:0.844155:0.141549:0.827721:0.132567:0.827721:0.000000
d:@0.141476:0.844155:0.150734:0.844155:0.150734:0.827748:0.141476:0.827748:0.000000
2:@0.150666:0.838088:0.155903:0.838088:0.155903:0.828507:0.150666:0.828507:0.000000
        = :@0.157202:0.835232:0.203791:0.835232:0.203791:0.818798:0.157202:0.818798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.220500:0.828428:0.229482:0.828428:0.229482:0.811994:0.220500:0.811994:0.000000
8:@0.203639:0.854902:0.212621:0.854902:0.212621:0.838469:0.203639:0.838469:0.000000
3:@0.221330:0.847270:0.230312:0.847270:0.230312:0.830836:0.221330:0.830836:0.000000
2:@0.221330:0.863662:0.230312:0.863662:0.230312:0.847228:0.221330:0.847228:0.000000
2:@0.238649:0.841441:0.244058:0.841441:0.244058:0.831007:0.238649:0.831007:0.000000
            =      .:@0.246256:0.835232:0.341681:0.835237:0.341681:0.818803:0.246256:0.818798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.311125:0.827762:0.320108:0.827762:0.320108:0.811328:0.311125:0.811328:0.000000
2:@0.311125:0.844155:0.320108:0.844155:0.320108:0.827721:0.311125:0.827721:0.000000
Así, el término general de la progresión geométrica está dado:@0.103197:0.880475:0.549632:0.880475:0.549632:0.864042:0.103197:0.864042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como   =  :@0.103197:0.910514:0.187243:0.910507:0.187243:0.894073:0.103197:0.894080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.149694:0.910514:0.158952:0.910514:0.158952:0.894108:0.149694:0.894108:0.000000
n:@0.158901:0.913679:0.164438:0.913679:0.164438:0.904114:0.158901:0.904114:0.000000
3:@0.212374:0.903782:0.221356:0.903782:0.221356:0.887348:0.212374:0.887348:0.000000
2:@0.212374:0.920174:0.221356:0.920174:0.221356:0.903740:0.212374:0.903740:0.000000
1:@0.189765:0.903782:0.198747:0.903782:0.198747:0.887348:0.189765:0.887348:0.000000
2:@0.189765:0.920174:0.198747:0.920174:0.198747:0.903740:0.189765:0.903740:0.000000
n:@0.227638:0.895432:0.233679:0.895432:0.233679:0.884998:0.227638:0.884998:0.000000
 , ...      .:@0.236562:0.910507:0.310678:0.910507:0.310678:0.894073:0.236562:0.894073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.260897:0.910507:0.270395:0.910507:0.270395:0.894101:0.260897:0.894101:0.000000
∈:@0.274470:0.910905:0.289106:0.910905:0.289106:0.894053:0.274470:0.894053:0.000000
ℕ:@0.293155:0.911089:0.307476:0.911089:0.307476:0.893435:0.293155:0.893435:0.000000
Nota que esta sucesión es estrictamente creciente.:@0.103210:0.937869:0.470245:0.937869:0.470245:0.921435:0.103210:0.921435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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
Donde::@0.744683:0.767243:0.795654:0.767243:0.795654:0.752089:0.744683:0.752089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otras formas de escribir :@0.741917:0.187395:0.902977:0.187395:0.902977:0.172455:0.741917:0.172455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los términos de una pro-:@0.741917:0.202524:0.905608:0.202524:0.905608:0.187584:0.741917:0.187584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gresión geométrica son::@0.741917:0.217652:0.902443:0.217652:0.902443:0.202713:0.741917:0.202713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Razón.:@0.741917:0.239930:0.788169:0.239930:0.788169:0.224776:0.741917:0.224776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si la razón es   > 1, la :@0.741917:0.262207:0.882013:0.262207:0.882013:0.247267:0.741917:0.247267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.830355:0.262207:0.835158:0.262207:0.835158:0.247293:0.830355:0.247293:0.000000
progresión es creciente, y :@0.741917:0.277336:0.914943:0.277336:0.914943:0.262396:0.741917:0.262396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decreciente cuando 0 < :@0.741917:0.292465:0.904418:0.292465:0.904418:0.277525:0.741917:0.277525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.741917:0.307594:0.746720:0.307594:0.746720:0.292679:0.741917:0.292679:0.000000
 < 1.:@0.746720:0.307594:0.775100:0.307594:0.775100:0.292654:0.746720:0.292654:0.000000:0.000000:0.000000:0.000000:0.000000
•  Se calcula dividiendo :@0.741917:0.329869:0.905303:0.329869:0.905303:0.314929:0.741917:0.314929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un término por el que :@0.760890:0.344998:0.911192:0.344998:0.911192:0.330058:0.760890:0.330058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
le precede.:@0.760890:0.360127:0.833864:0.360127:0.833864:0.345187:0.760890:0.345187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  La razón puede ser :@0.741917:0.382404:0.890410:0.382404:0.890410:0.367464:0.741917:0.367464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un número positivo o :@0.760890:0.397533:0.908531:0.397533:0.908531:0.382593:0.760890:0.382593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
negativo.:@0.760890:0.412662:0.822303:0.412662:0.822303:0.397722:0.760890:0.397722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Notación y término :@0.741914:0.434939:0.879832:0.434939:0.879832:0.419785:0.741914:0.419785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n-ésimo.:@0.741914:0.450068:0.801771:0.450068:0.801771:0.434914:0.741914:0.434914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.741914:0.472346:0.750331:0.472346:0.750331:0.457431:0.741914:0.457431:0.000000
 = primer término;   = :@0.750331:0.472346:0.897838:0.472346:0.897838:0.457406:0.750331:0.457406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.875733:0.472346:0.880535:0.472346:0.880535:0.457431:0.875733:0.457431:0.000000
razón o diferencia;    = :@0.741914:0.487475:0.896585:0.487475:0.896585:0.472535:0.741914:0.472535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.870647:0.487475:0.879282:0.487475:0.879282:0.472560:0.870647:0.472560:0.000000
número de términos:@0.741914:0.502604:0.879347:0.502604:0.879347:0.487664:0.741914:0.487664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Término n-ésimo  :@0.741914:0.524881:0.855888:0.524881:0.855888:0.509941:0.741914:0.509941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un =   •   :@0.741914:0.540010:0.802825:0.540010:0.802825:0.525070:0.741914:0.525070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a r:@0.776569:0.540010:0.799578:0.540010:0.799578:0.525095:0.776569:0.525095:0.000000:0.000000:0.000000
n – 1:@0.802408:0.534493:0.820574:0.534493:0.820574:0.525783:0.802408:0.525783:0.000000:0.000000:0.000000:0.000000:0.000000
, el último :@0.820330:0.540006:0.889190:0.540006:0.889190:0.525066:0.820330:0.525066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
término:   = :@0.741915:0.555135:0.822556:0.555135:0.822556:0.540195:0.741915:0.540195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.801806:0.555135:0.805253:0.555135:0.805253:0.540220:0.801806:0.540220:0.000000
ar :@0.822556:0.555135:0.838788:0.555135:0.838788:0.540220:0.822556:0.540220:0.000000:0.000000:0.000000
n:@0.838788:0.549622:0.843822:0.549622:0.843822:0.540927:0.838788:0.540927:0.000000
–1:@0.843822:0.549622:0.853460:0.549622:0.853460:0.540912:0.843822:0.540912:0.000000:0.000000
Suma de los primeros  :@0.741917:0.577412:0.899163:0.577412:0.899163:0.562258:0.741917:0.562258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos.:@0.741917:0.592541:0.807530:0.592541:0.807530:0.577387:0.741917:0.577387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= ⋅:@0.761025:0.621493:0.787714:0.621493:0.787714:0.607439:0.761025:0.607439:0.000000:0.000000:0.000000
⎛:@0.788934:0.612805:0.795296:0.612805:0.795296:0.598751:0.788934:0.598751:0.000000
⎝:@0.788934:0.631245:0.795296:0.631245:0.795296:0.617191:0.788934:0.617191:0.000000
⎜:@0.788934:0.626003:0.795296:0.626003:0.795296:0.611949:0.788934:0.611949:0.000000
⎞:@0.830821:0.612805:0.837182:0.612805:0.837182:0.598751:0.830821:0.598751:0.000000
⎠:@0.830821:0.631245:0.837182:0.631245:0.837182:0.617191:0.830821:0.617191:0.000000
⎟:@0.830821:0.626003:0.837182:0.626003:0.837182:0.611949:0.830821:0.611949:0.000000
=:@0.859945:0.621497:0.869040:0.621497:0.869040:0.607443:0.859945:0.607443:0.000000
–1:@0.814207:0.612796:0.831801:0.612796:0.831801:0.598006:0.814207:0.598006:0.000000:0.000000
–1:@0.810725:0.630350:0.828319:0.630350:0.828319:0.615559:0.810725:0.615559:0.000000:0.000000
;:@0.840429:0.620889:0.843311:0.620889:0.843311:0.606099:0.840429:0.606099:0.000000
,:@0.844852:0.620889:0.847735:0.620889:0.847735:0.606099:0.844852:0.606099:0.000000
–:@0.884566:0.612798:0.892850:0.612798:0.892850:0.598007:0.884566:0.598007:0.000000
–1:@0.885413:0.630351:0.903007:0.630351:0.903007:0.615561:0.885413:0.615561:0.000000:0.000000
S:@0.744598:0.620890:0.751854:0.620890:0.751854:0.606125:0.744598:0.606125:0.000000
a:@0.773407:0.620890:0.781740:0.620890:0.781740:0.606125:0.773407:0.606125:0.000000
r:@0.799145:0.612799:0.803900:0.612799:0.803900:0.598034:0.799145:0.598034:0.000000
r:@0.802581:0.630352:0.807335:0.630352:0.807335:0.615587:0.802581:0.615587:0.000000
S:@0.849265:0.620891:0.856521:0.620891:0.856521:0.606126:0.849265:0.606126:0.000000
lr a:@0.873318:0.612800:0.903771:0.612800:0.903771:0.598035:0.873318:0.598035:0.000000:0.000000:0.000000:0.000000
r:@0.877270:0.630354:0.882025:0.630354:0.882025:0.615588:0.877270:0.615588:0.000000
n:@0.751800:0.622690:0.756754:0.622690:0.756754:0.614133:0.751800:0.614133:0.000000
n:@0.805452:0.605883:0.810406:0.605883:0.810406:0.597326:0.805452:0.597326:0.000000
Aplicación de progre-:@0.741917:0.651433:0.892420:0.651433:0.892420:0.636279:0.741917:0.636279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siones en finanzas: valor :@0.741915:0.666562:0.913168:0.666562:0.913168:0.651408:0.741915:0.651408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
futuro.:@0.741915:0.681691:0.788335:0.681691:0.788335:0.666537:0.741915:0.666537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Define:@0.741915:0.837620:0.787933:0.837620:0.787933:0.822466:0.741915:0.822466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 con tus palabras :@0.787933:0.837620:0.904217:0.837620:0.904217:0.822680:0.787933:0.822680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
qué es una progresión :@0.741915:0.852749:0.894794:0.852749:0.894794:0.837809:0.741915:0.837809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
geométrica.:@0.741915:0.867878:0.821550:0.867878:0.821550:0.852938:0.741915:0.852938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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