163:@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
Ejercicio 7:@0.073089:0.136836:0.149492:0.136836:0.149492:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado :@0.073089:0.172796:0.116383:0.172796:0.116383:0.156363:0.073089:0.156363:0.000000:0.000000:0.000000:0.000000:0.000000
α :@0.116143:0.172796:0.130115:0.172796:0.130115:0.156127:0.116143:0.156127:0.000000:0.000000
∈ ℝ:@0.130041:0.173379:0.163266:0.173379:0.163266:0.155725:0.130041:0.155725:0.000000:0.000000:0.000000
   constante no nula, la sucesión definida como  :@0.145650:0.172796:0.497628:0.172796:0.497628:0.156363:0.145650:0.156363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.507739:0.163935:0.516998:0.163935:0.516998:0.147529:0.507739:0.147529:0.000000
0:@0.516922:0.167108:0.522159:0.167108:0.522159:0.157527:0.516922:0.157527:0.000000
     dado,:@0.522111:0.163936:0.603907:0.163936:0.603907:0.147502:0.522111:0.147502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.526068:0.164518:0.559294:0.164518:0.559294:0.146864:0.526068:0.146864:0.000000:0.000000:0.000000
a:@0.507735:0.180578:0.516994:0.180578:0.516994:0.164172:0.507735:0.164172:0.000000
n:@0.516793:0.183750:0.522330:0.183750:0.522330:0.174185:0.516793:0.174185:0.000000
+1:@0.522212:0.183750:0.533727:0.183750:0.533727:0.174169:0.522212:0.174169:0.000000:0.000000
 = :@0.533605:0.180578:0.552234:0.180578:0.552234:0.164144:0.533605:0.164144:0.000000:0.000000:0.000000
α:@0.552013:0.180578:0.562155:0.180578:0.562155:0.163908:0.552013:0.163908:0.000000
a:@0.562450:0.180578:0.571708:0.180578:0.571708:0.164172:0.562450:0.164172:0.000000
n:@0.571506:0.183750:0.577258:0.183750:0.577258:0.174169:0.571506:0.174169:0.000000
,     = 0, 1, ... :@0.577135:0.180578:0.663760:0.180578:0.663760:0.164144:0.577135:0.164144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.591585:0.180578:0.601083:0.180578:0.601083:0.164172:0.591585:0.164172:0.000000
cinco de sus términos se describen a continuación::@0.073089:0.196592:0.442401:0.196592:0.442401:0.180158:0.073089:0.180158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.073089:0.223954:0.082348:0.223954:0.082348:0.207548:0.073089:0.207548:0.000000
1:@0.082152:0.227127:0.087389:0.227127:0.087389:0.217546:0.082152:0.217546:0.000000
 = :@0.087267:0.223955:0.105895:0.223955:0.105895:0.207521:0.087267:0.207521:0.000000:0.000000:0.000000
α:@0.105674:0.223955:0.115817:0.223955:0.115817:0.207285:0.105674:0.207285:0.000000
a:@0.116111:0.223955:0.125370:0.223955:0.125370:0.207549:0.116111:0.207549:0.000000
0:@0.125167:0.227127:0.130404:0.227127:0.130404:0.217546:0.125167:0.217546:0.000000
,      = :@0.130282:0.223955:0.181369:0.223955:0.181369:0.207521:0.130282:0.207521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.148561:0.223955:0.157819:0.223955:0.157819:0.207549:0.148561:0.207549:0.000000
2:@0.157625:0.227127:0.162862:0.227127:0.162862:0.217546:0.157625:0.217546:0.000000
α:@0.181148:0.223955:0.191291:0.223955:0.191291:0.207285:0.181148:0.207285:0.000000
a:@0.191585:0.223955:0.200844:0.223955:0.200844:0.207549:0.191585:0.207549:0.000000
1:@0.200640:0.227127:0.205877:0.227127:0.205877:0.217546:0.200640:0.217546:0.000000
 = :@0.205755:0.223955:0.224384:0.223955:0.224384:0.207521:0.205755:0.207521:0.000000:0.000000:0.000000
a:@0.224163:0.223955:0.233422:0.223955:0.233422:0.207549:0.224163:0.207549:0.000000
0:@0.233222:0.227127:0.238459:0.227127:0.238459:0.217546:0.233222:0.217546:0.000000
α:@0.238338:0.223955:0.248480:0.223955:0.248480:0.207285:0.238338:0.207285:0.000000
2:@0.248770:0.217891:0.254007:0.217891:0.254007:0.208310:0.248770:0.208310:0.000000
,     = :@0.253885:0.223955:0.301150:0.223955:0.301150:0.207521:0.253885:0.207521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.268335:0.223955:0.277594:0.223955:0.277594:0.207549:0.268335:0.207549:0.000000
3:@0.277407:0.227127:0.282643:0.227127:0.282643:0.217546:0.277407:0.217546:0.000000
α:@0.300929:0.223955:0.311072:0.223955:0.311072:0.207285:0.300929:0.207285:0.000000
a:@0.311366:0.223955:0.320625:0.223955:0.320625:0.207549:0.311366:0.207549:0.000000
2:@0.320423:0.227127:0.325659:0.227127:0.325659:0.217546:0.320423:0.217546:0.000000
 = :@0.325536:0.223955:0.344165:0.223955:0.344165:0.207521:0.325536:0.207521:0.000000:0.000000:0.000000
a:@0.343944:0.223955:0.353203:0.223955:0.353203:0.207549:0.343944:0.207549:0.000000
0:@0.353005:0.227127:0.358242:0.227127:0.358242:0.217546:0.353005:0.217546:0.000000
α:@0.358119:0.223955:0.368261:0.223955:0.368261:0.207285:0.358119:0.207285:0.000000
3 :@0.368551:0.217891:0.376020:0.217891:0.376020:0.208310:0.368551:0.208310:0.000000:0.000000
,     = :@0.375894:0.223955:0.423159:0.223955:0.423159:0.207521:0.375894:0.207521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.390343:0.223955:0.399602:0.223955:0.399602:0.207549:0.390343:0.207549:0.000000
4:@0.399416:0.227127:0.404653:0.227127:0.404653:0.217546:0.399416:0.217546:0.000000
α:@0.422938:0.223955:0.433080:0.223955:0.433080:0.207285:0.422938:0.207285:0.000000
a:@0.433375:0.223955:0.442633:0.223955:0.442633:0.207549:0.433375:0.207549:0.000000
3:@0.442431:0.227127:0.447668:0.227127:0.447668:0.217546:0.442431:0.217546:0.000000
 = :@0.447546:0.223955:0.466175:0.223955:0.466175:0.207521:0.447546:0.207521:0.000000:0.000000:0.000000
a:@0.465954:0.223955:0.475213:0.223955:0.475213:0.207549:0.465954:0.207549:0.000000
0:@0.475013:0.227127:0.480250:0.227127:0.480250:0.217546:0.475013:0.217546:0.000000
α:@0.480129:0.223955:0.490271:0.223955:0.490271:0.207285:0.480129:0.207285:0.000000
4:@0.490561:0.217891:0.495798:0.217891:0.495798:0.208310:0.490561:0.208310:0.000000
,:@0.495675:0.223955:0.498878:0.223955:0.498878:0.207521:0.495675:0.207521:0.000000
a:@0.073081:0.251317:0.082340:0.251317:0.082340:0.234911:0.073081:0.234911:0.000000
n:@0.082153:0.254491:0.087690:0.254491:0.087690:0.244926:0.082153:0.244926:0.000000
+1:@0.087572:0.254491:0.099087:0.254491:0.099087:0.244910:0.087572:0.244910:0.000000:0.000000
 = :@0.098965:0.251318:0.117593:0.251318:0.117593:0.234884:0.098965:0.234884:0.000000:0.000000:0.000000
α:@0.117372:0.251318:0.127515:0.251318:0.127515:0.234649:0.117372:0.234649:0.000000
a:@0.127809:0.251318:0.137068:0.251318:0.137068:0.234912:0.127809:0.234912:0.000000
n:@0.136865:0.254491:0.142618:0.254491:0.142618:0.244910:0.136865:0.244910:0.000000
 = :@0.142496:0.251318:0.161125:0.251318:0.161125:0.234884:0.142496:0.234884:0.000000:0.000000:0.000000
a:@0.160904:0.251318:0.170163:0.251318:0.170163:0.234912:0.160904:0.234912:0.000000
0:@0.169965:0.254491:0.175202:0.254491:0.175202:0.244910:0.169965:0.244910:0.000000
α:@0.175079:0.251318:0.185221:0.251318:0.185221:0.234649:0.175079:0.234649:0.000000
n:@0.185511:0.245254:0.191048:0.245254:0.191048:0.235690:0.185511:0.235690:0.000000
+1:@0.190930:0.245254:0.202445:0.245254:0.202445:0.235673:0.190930:0.235673:0.000000:0.000000
,     = 0, 1, ...:@0.202323:0.251318:0.284917:0.251318:0.284917:0.234884:0.202323:0.234884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.216773:0.251318:0.226271:0.251318:0.226271:0.234912:0.216773:0.234912:0.000000
1.3 Sucesiones monótonas:@0.073068:0.295322:0.282354:0.295322:0.282354:0.278375:0.073068:0.278375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición.:@0.073068:0.322684:0.154774:0.322684:0.154774:0.306014:0.073068:0.306014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.154649:0.322684:0.158459:0.322684:0.158459:0.305737:0.154649:0.305737:0.000000
Sea ( ) una sucesión real.:@0.158385:0.322684:0.344645:0.322686:0.344645:0.306253:0.158385:0.306250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.192807:0.322684:0.202066:0.322684:0.202066:0.306278:0.192807:0.306278:0.000000
n:@0.202027:0.325859:0.207565:0.325859:0.207565:0.316294:0.202027:0.316294:0.000000
i.:@0.073089:0.354631:0.080065:0.354631:0.080065:0.338197:0.073089:0.338197:0.000000:0.000000
Se dice que ( ) es creciente si y solo si   ≤ :@0.103290:0.354631:0.418950:0.354631:0.418950:0.338197:0.103290:0.338197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.196450:0.354631:0.205708:0.354631:0.205708:0.338225:0.196450:0.338225:0.000000
n:@0.205643:0.357804:0.211181:0.357804:0.211181:0.348239:0.205643:0.348239:0.000000
a:@0.385367:0.354631:0.394626:0.354631:0.394626:0.338225:0.385367:0.338225:0.000000
n:@0.394565:0.357804:0.400103:0.357804:0.400103:0.348239:0.394565:0.348239:0.000000
a:@0.418858:0.354631:0.428117:0.354631:0.428117:0.338225:0.418858:0.338225:0.000000
n:@0.428048:0.357804:0.433586:0.357804:0.433586:0.348239:0.428048:0.348239:0.000000
+1:@0.433543:0.357804:0.445133:0.357804:0.445133:0.348223:0.433543:0.348223:0.000000:0.000000
,  :@0.445624:0.354631:0.456742:0.354631:0.456742:0.338197:0.445624:0.338197:0.000000:0.000000:0.000000
∀:@0.456650:0.355214:0.468927:0.355214:0.468927:0.337559:0.456650:0.337559:0.000000
n:@0.468835:0.354631:0.478333:0.354631:0.478333:0.338225:0.468835:0.338225:0.000000
    .:@0.478260:0.354631:0.509571:0.354631:0.509571:0.338197:0.478260:0.338197:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.482214:0.355030:0.496850:0.355030:0.496850:0.338178:0.482214:0.338178:0.000000
Ι:@0.500053:0.355214:0.505782:0.355214:0.508659:0.337559:0.502930:0.337559:0.000000
ii.:@0.073089:0.375856:0.082808:0.375856:0.082808:0.359422:0.073089:0.359422:0.000000:0.000000:0.000000
Se dice que ( ) es estrictamente creciente si y solo si   < :@0.103806:0.375856:0.491715:0.375856:0.491715:0.359422:0.103806:0.359422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.190265:0.375856:0.199524:0.375856:0.199524:0.359450:0.190265:0.359450:0.000000
n:@0.198943:0.379028:0.204480:0.379028:0.204480:0.369463:0.198943:0.369463:0.000000
a:@0.461347:0.375856:0.470606:0.375856:0.470606:0.359450:0.461347:0.359450:0.000000
n:@0.470023:0.379028:0.475561:0.379028:0.475561:0.369463:0.470023:0.369463:0.000000
a:@0.491071:0.375856:0.500330:0.375856:0.500330:0.359450:0.491071:0.359450:0.000000
n:@0.499709:0.379028:0.505247:0.379028:0.505247:0.369463:0.499709:0.369463:0.000000
+1:@0.504882:0.379028:0.516150:0.379028:0.516150:0.369447:0.504882:0.369447:0.000000:0.000000
,  :@0.516318:0.375856:0.526331:0.375856:0.526331:0.359422:0.516318:0.359422:0.000000:0.000000:0.000000
∀:@0.525687:0.376438:0.537965:0.376438:0.537965:0.358784:0.525687:0.358784:0.000000
n:@0.537320:0.375856:0.546818:0.375856:0.546818:0.359450:0.537320:0.359450:0.000000
    .:@0.546193:0.375856:0.575430:0.375856:0.575430:0.359422:0.546193:0.359422:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.549595:0.376254:0.564231:0.376254:0.564231:0.359402:0.549595:0.359402:0.000000
Ι:@0.566355:0.376438:0.572083:0.376438:0.574960:0.358784:0.569232:0.358784:0.000000
iii. Se dice que ( ) es decreciente si y solo si :@0.073089:0.397080:0.404426:0.397080:0.404426:0.380647:0.073089:0.380647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.196450:0.397080:0.205709:0.397080:0.205709:0.380674:0.196450:0.380674:0.000000
n:@0.205643:0.400253:0.211181:0.400253:0.211181:0.390688:0.205643:0.390688:0.000000
a:@0.404161:0.397080:0.413419:0.397080:0.413419:0.380674:0.404161:0.380674:0.000000
n:@0.413346:0.400253:0.418883:0.400253:0.418883:0.390688:0.413346:0.390688:0.000000
+1:@0.418840:0.400253:0.430430:0.400253:0.430430:0.390672:0.418840:0.390672:0.000000:0.000000
 ≤  ,  :@0.430920:0.397080:0.475520:0.397080:0.475520:0.380647:0.430920:0.380647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.449713:0.397080:0.458972:0.397080:0.458972:0.380674:0.449713:0.380674:0.000000
n:@0.458904:0.400253:0.464441:0.400253:0.464441:0.390688:0.458904:0.390688:0.000000
∀:@0.475428:0.397663:0.487706:0.397663:0.487706:0.380009:0.475428:0.380009:0.000000
n:@0.487614:0.397080:0.497112:0.397080:0.497112:0.380674:0.487614:0.380674:0.000000
    .:@0.497039:0.397080:0.528351:0.397080:0.528351:0.380647:0.497039:0.380647:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.500994:0.397479:0.515631:0.397479:0.515631:0.380627:0.500994:0.380627:0.000000
Ι:@0.518834:0.397663:0.524562:0.397663:0.527439:0.380009:0.521711:0.380009:0.000000
iv. Se dice que ( ) es estrictamente decreciente si y solo si :@0.073089:0.418304:0.509121:0.418304:0.509121:0.401870:0.073089:0.401870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.196450:0.418304:0.205709:0.418304:0.205709:0.401898:0.196450:0.401898:0.000000
n:@0.205643:0.421476:0.211181:0.421476:0.211181:0.411911:0.205643:0.411911:0.000000
a:@0.508769:0.418304:0.518028:0.418304:0.518028:0.401898:0.508769:0.401898:0.000000
n:@0.517968:0.421476:0.523505:0.421476:0.523505:0.411911:0.517968:0.411911:0.000000
+1:@0.523462:0.421476:0.535052:0.421476:0.535052:0.411895:0.523462:0.411895:0.000000:0.000000
 <  , :@0.535541:0.418304:0.576720:0.418304:0.576720:0.401870:0.535541:0.401870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.554335:0.418304:0.563594:0.418304:0.563594:0.401898:0.554335:0.401898:0.000000
n:@0.563526:0.421476:0.569063:0.421476:0.569063:0.411911:0.563526:0.411911:0.000000
∀:@0.576628:0.418886:0.588906:0.418886:0.588906:0.401232:0.576628:0.401232:0.000000
n:@0.588814:0.418304:0.598312:0.418304:0.598312:0.401898:0.588814:0.401898:0.000000
    .:@0.598238:0.418304:0.629557:0.418304:0.629557:0.401870:0.598238:0.401870:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.602201:0.418702:0.616837:0.418702:0.616837:0.401850:0.602201:0.401850:0.000000
Ι:@0.620040:0.418886:0.625768:0.418886:0.628646:0.401232:0.622917:0.401232:0.000000
v.:@0.073089:0.439528:0.083912:0.439528:0.083912:0.423095:0.073089:0.423095:0.000000:0.000000
Se dice que la sucesión ( ) es monótona si es creciente o decreciente.:@0.103291:0.439528:0.612147:0.439528:0.612147:0.423095:0.103291:0.423095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.279963:0.439528:0.289222:0.439528:0.289222:0.423122:0.279963:0.423122:0.000000
n:@0.289147:0.442701:0.294684:0.442701:0.294684:0.433136:0.289147:0.433136:0.000000
Ejercicio 8:@0.073096:0.474033:0.149499:0.474033:0.149499:0.457363:0.073096:0.457363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.:@0.073089:0.504932:0.084575:0.504932:0.084575:0.488498:0.073089:0.488498:0.000000:0.000000
La sucesión ( ), cuyo término general está definido como   =   ,     :@0.103291:0.504932:0.630871:0.504937:0.630871:0.488503:0.103291:0.488498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.197941:0.504932:0.207200:0.504932:0.207200:0.488526:0.197941:0.488526:0.000000
n:@0.207205:0.508104:0.212742:0.508104:0.212742:0.498540:0.207205:0.498540:0.000000
a:@0.536032:0.504932:0.545291:0.504932:0.545291:0.488526:0.536032:0.488526:0.000000
n:@0.545296:0.508104:0.550833:0.508104:0.550833:0.498540:0.545296:0.498540:0.000000
1:@0.573385:0.497462:0.582368:0.497462:0.582368:0.481028:0.573385:0.481028:0.000000
n:@0.573127:0.513854:0.582626:0.513854:0.582626:0.497448:0.573127:0.497448:0.000000
n:@0.597149:0.504937:0.606647:0.504937:0.606647:0.488531:0.597149:0.488531:0.000000
∈ ℤ:@0.611138:0.505520:0.643959:0.505520:0.643959:0.487865:0.611138:0.487865:0.000000:0.000000:0.000000
+:@0.643967:0.496347:0.650363:0.496347:0.650363:0.486766:0.643967:0.486766:0.000000
, es una:@0.650368:0.504932:0.706307:0.504932:0.706307:0.488498:0.650368:0.488498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sucesión estrictamente decreciente.:@0.103212:0.525110:0.364277:0.525110:0.364277:0.508677:0.103212:0.508677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En efecto, si     :@0.103212:0.548853:0.225418:0.548853:0.225418:0.532419:0.103212:0.532419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.192395:0.548853:0.201893:0.548853:0.201893:0.532447:0.192395:0.532447:0.000000
∈ ℤ:@0.205777:0.549435:0.237990:0.549435:0.237990:0.531781:0.205777:0.531781:0.000000:0.000000:0.000000
+:@0.237881:0.540265:0.244277:0.540265:0.244277:0.530684:0.237881:0.530684:0.000000
, entonces   <   + 1 y, en consecuencia, :@0.244230:0.548850:0.536180:0.548850:0.536180:0.532416:0.244230:0.532416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.322645:0.548850:0.332143:0.548850:0.332143:0.532444:0.322645:0.532444:0.000000
n:@0.350863:0.548850:0.360361:0.548850:0.360361:0.532444:0.350863:0.532444:0.000000
1:@0.548053:0.541380:0.557036:0.541380:0.557036:0.524946:0.548053:0.524946:0.000000
n:@0.537893:0.557773:0.547391:0.557773:0.547391:0.541366:0.537893:0.541366:0.000000
+1:@0.547317:0.557773:0.567197:0.557773:0.567197:0.541339:0.547317:0.541339:0.000000:0.000000
 <  .:@0.569056:0.548855:0.605206:0.548855:0.605206:0.532421:0.569056:0.532421:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.590480:0.541380:0.599463:0.541380:0.599463:0.524946:0.590480:0.524946:0.000000
n:@0.590223:0.557773:0.599721:0.557773:0.599721:0.541366:0.590223:0.541366:0.000000
De la definición de ( ) se concluye que :@0.103204:0.579754:0.419294:0.579744:0.419294:0.563310:0.103204:0.563320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.262077:0.579754:0.271335:0.579754:0.271335:0.563348:0.262077:0.563348:0.000000
n:@0.271566:0.582916:0.277104:0.582916:0.277104:0.573351:0.271566:0.573351:0.000000
a:@0.421232:0.579744:0.430491:0.579744:0.430491:0.563337:0.421232:0.563337:0.000000
n:@0.430716:0.582916:0.436253:0.582916:0.436253:0.573351:0.430716:0.573351:0.000000
+1:@0.436382:0.582916:0.448176:0.582916:0.448176:0.573335:0.436382:0.573335:0.000000:0.000000
 ≤  ; o sea, ( ) es estrictamente:@0.448865:0.579744:0.706418:0.579744:0.706418:0.563310:0.448865:0.563310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.472224:0.579744:0.481483:0.579744:0.481483:0.563337:0.472224:0.563337:0.000000
n:@0.481697:0.582916:0.487234:0.582916:0.487234:0.573351:0.481697:0.573351:0.000000
a:@0.552654:0.579744:0.561912:0.579744:0.561912:0.563337:0.552654:0.563337:0.000000
n:@0.562125:0.582916:0.567662:0.582916:0.567662:0.573351:0.562125:0.573351:0.000000
decreciente.:@0.103212:0.599922:0.192062:0.599922:0.192062:0.583488:0.103212:0.583488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b. La sucesión   1 –:@0.073089:0.630809:0.222851:0.630528:0.222851:0.614094:0.073089:0.614375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.233253:0.622666:0.242235:0.622666:0.242235:0.606232:0.233253:0.606232:0.000000
n:@0.232995:0.639058:0.242493:0.639058:0.242493:0.622652:0.232995:0.622652:0.000000
  es estrictamente creciente, pues si     :@0.251365:0.630809:0.544243:0.630809:0.544243:0.614375:0.251365:0.614375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.511220:0.630809:0.520719:0.630809:0.520719:0.614403:0.511220:0.614403:0.000000
∈ ℤ:@0.524603:0.631391:0.556815:0.631391:0.556815:0.613737:0.524603:0.613737:0.000000:0.000000:0.000000
+:@0.556710:0.622223:0.563106:0.622223:0.563106:0.612642:0.556710:0.612642:0.000000
, :@0.563059:0.630809:0.570293:0.630809:0.570293:0.614375:0.563059:0.614375:0.000000:0.000000
entonces   <   + 1, y se tienen las siguientes equivalencias: :@0.103209:0.658129:0.535275:0.658129:0.535275:0.641695:0.103209:0.641695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.174555:0.658129:0.184053:0.658129:0.184053:0.641723:0.174555:0.641723:0.000000
n:@0.202773:0.658129:0.212272:0.658129:0.212272:0.641723:0.202773:0.641723:0.000000
1:@0.145442:0.681551:0.154424:0.681551:0.154424:0.665117:0.145442:0.665117:0.000000
n:@0.135281:0.697943:0.144779:0.697943:0.144779:0.681537:0.135281:0.681537:0.000000
+1:@0.144705:0.697943:0.164585:0.697943:0.164585:0.681510:0.144705:0.681510:0.000000:0.000000
<     –:@0.170402:0.689026:0.233360:0.689021:0.233360:0.672587:0.170402:0.672592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.187869:0.681551:0.196851:0.681551:0.196851:0.665117:0.187869:0.665117:0.000000
n:@0.187611:0.697943:0.197109:0.697943:0.197109:0.681537:0.187611:0.681537:0.000000
1:@0.239846:0.681551:0.248828:0.681551:0.248828:0.665117:0.239846:0.665117:0.000000
n:@0.239588:0.697943:0.249086:0.697943:0.249086:0.681537:0.239588:0.681537:0.000000
< – :@0.255326:0.689026:0.283342:0.689026:0.283342:0.672592:0.255326:0.672592:0.000000:0.000000:0.000000:0.000000
1:@0.295347:0.682445:0.304330:0.682445:0.304330:0.666011:0.295347:0.666011:0.000000
n:@0.285186:0.698837:0.294684:0.698837:0.294684:0.682431:0.285186:0.682431:0.000000
+1:@0.294611:0.698837:0.314490:0.698837:0.314490:0.682403:0.294611:0.682403:0.000000:0.000000
1 –   < 1 – :@0.341117:0.689021:0.426023:0.689019:0.426023:0.672585:0.341117:0.672587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.369660:0.682445:0.378643:0.682445:0.378643:0.666011:0.369660:0.666011:0.000000
n:@0.369403:0.698837:0.378901:0.698837:0.378901:0.682431:0.369403:0.682431:0.000000
1:@0.438013:0.681551:0.446996:0.681551:0.446996:0.665117:0.438013:0.665117:0.000000
n:@0.427852:0.697943:0.437350:0.697943:0.437350:0.681537:0.427852:0.681537:0.000000
+1:@0.437277:0.697943:0.457157:0.697943:0.457157:0.681510:0.437277:0.681510:0.000000:0.000000
   < :@0.479826:0.689021:0.516035:0.689021:0.516035:0.672587:0.479826:0.672587:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.483784:0.689021:0.493042:0.689021:0.493042:0.672615:0.483784:0.672615:0.000000
n:@0.492601:0.692194:0.498138:0.692194:0.498138:0.682629:0.492601:0.682629:0.000000
a:@0.515575:0.689021:0.524833:0.689021:0.524833:0.672615:0.515575:0.672615:0.000000
n:@0.524397:0.692194:0.529934:0.692194:0.529934:0.682629:0.524397:0.682629:0.000000
+1:@0.529677:0.692194:0.541052:0.692194:0.541052:0.682612:0.529677:0.682612:0.000000:0.000000
.:@0.541326:0.689021:0.544529:0.689021:0.544529:0.672587:0.541326:0.672587:0.000000
Recuerda que si a una desigualdad se la multiplica por –1, la desigualdad cambia :@0.103215:0.719919:0.710844:0.719919:0.710844:0.703486:0.103215:0.703486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de sentido. Además, si a una desigualdad se le suma en ambos miembros el :@0.103215:0.740098:0.710469:0.740098:0.710469:0.723664:0.103215:0.723664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mismo número real, la desigualdad se conserva.:@0.103215:0.760276:0.461227:0.760276:0.461227:0.743842:0.103215:0.743842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c.:@0.073089:0.791152:0.084041:0.791152:0.084041:0.774718:0.073089:0.774718:0.000000:0.000000
Considera la sucesión ( ), definida como   =   + 1 + (–1) ,       . El recorrido de esta:@0.103475:0.791152:0.706237:0.791152:0.706237:0.774718:0.103475:0.774718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.262477:0.791152:0.271791:0.791152:0.271791:0.774745:0.262477:0.774745:0.000000
p:@0.271521:0.794324:0.276919:0.794324:0.276919:0.784759:0.271521:0.784759:0.000000
u:@0.393371:0.791152:0.402685:0.791152:0.402685:0.774745:0.393371:0.774745:0.000000
p:@0.402420:0.794324:0.407818:0.794324:0.407818:0.784759:0.402420:0.784759:0.000000
p:@0.425018:0.791152:0.434276:0.791152:0.434276:0.774745:0.425018:0.774745:0.000000
p:@0.504206:0.785088:0.509603:0.785088:0.509603:0.775523:0.504206:0.775523:0.000000
p:@0.519037:0.791152:0.528296:0.791152:0.528296:0.774745:0.519037:0.774745:0.000000
∈:@0.531365:0.791550:0.546001:0.791550:0.546001:0.774698:0.531365:0.774698:0.000000
ℕ:@0.549042:0.791734:0.563363:0.791734:0.563363:0.774080:0.549042:0.774080:0.000000
sucesión es el conjunto::@0.103200:0.811330:0.276387:0.811330:0.276387:0.794896:0.103200:0.794896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{  + 1 + (–1)  |      } = {2, 1, 4, 3, ... ,   + 1 + (–1) , ...}.:@0.202047:0.842228:0.577420:0.842217:0.577420:0.825783:0.202047:0.825794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.206852:0.842228:0.216110:0.842228:0.216110:0.825822:0.206852:0.825822:0.000000
p:@0.289964:0.836153:0.295361:0.836153:0.295361:0.826588:0.289964:0.826588:0.000000
p:@0.306940:0.842217:0.316199:0.842217:0.316199:0.825811:0.306940:0.825811:0.000000
∈:@0.319713:0.842615:0.334349:0.842615:0.334349:0.825763:0.319713:0.825763:0.000000
ℕ:@0.337859:0.842799:0.352180:0.842799:0.352180:0.825145:0.337859:0.825145:0.000000
p:@0.464575:0.842217:0.473834:0.842217:0.473834:0.825811:0.464575:0.825811:0.000000
p:@0.547685:0.836153:0.553083:0.836153:0.553083:0.826588:0.547685:0.826588:0.000000
Esta no es una sucesión creciente ni decreciente; simplemente es una sucesión real.:@0.103212:0.873115:0.706821:0.873115:0.706821:0.856681:0.103212:0.856681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d. La sucesión (– ) es estrictamente decreciente, pues::@0.073089:0.904003:0.478922:0.904003:0.478922:0.887569:0.073089:0.887569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.205064:0.904003:0.214562:0.904003:0.214562:0.887597:0.205064:0.887597:0.000000
n:@0.103210:0.924175:0.112708:0.924175:0.112708:0.907769:0.103210:0.907769:0.000000
 <   + 1   –(  + 1) < –  :@0.112634:0.924175:0.297040:0.924175:0.297040:0.907741:0.112634:0.907741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.131428:0.924175:0.140926:0.924175:0.140926:0.907769:0.131428:0.907769:0.000000
n:@0.207231:0.924175:0.216730:0.924175:0.216730:0.907769:0.207231:0.907769:0.000000
n,  n:@0.277068:0.924175:0.318650:0.924175:0.318650:0.907769:0.277068:0.907769:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.296967:0.924757:0.309244:0.924757:0.309244:0.907103:0.296967:0.907103:0.000000
    .:@0.318577:0.924175:0.358464:0.924175:0.358464:0.907741:0.318577:0.907741:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.322526:0.924573:0.337162:0.924573:0.337162:0.907722:0.322526:0.907722:0.000000
ℕ:@0.341032:0.924757:0.355353:0.924757:0.355353:0.907103:0.341032:0.907103:0.000000
Interdisciplinaria :@0.740294:0.262863:0.863703:0.262863:0.863703:0.247457:0.740294:0.247457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y :@0.740294:0.277992:0.833204:0.277992:0.833204:0.263052:0.740294:0.263052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biología:@0.740294:0.293121:0.793969:0.293121:0.793969:0.278181:0.740294:0.278181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El estudio de sucesiones :@0.741105:0.323415:0.906871:0.323415:0.906871:0.308475:0.741105:0.308475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es ampliamente utilizado :@0.741105:0.338544:0.912559:0.338544:0.912559:0.323604:0.741105:0.323604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en biología para analizar la :@0.741105:0.353673:0.921662:0.353673:0.921662:0.338733:0.741105:0.338733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reproducción bacteriana, :@0.741105:0.368802:0.911772:0.368802:0.911772:0.353862:0.741105:0.353862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
considerando que una :@0.741105:0.383931:0.895425:0.383931:0.895425:0.368991:0.741105:0.368991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bacteria se reproduce por :@0.741105:0.399060:0.916341:0.399060:0.916341:0.384120:0.741105:0.384120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bipartición. En condi-:@0.741105:0.414189:0.883477:0.414189:0.883477:0.399249:0.741105:0.399249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones muy favorables, :@0.741105:0.429318:0.895875:0.429318:0.895875:0.414378:0.741105:0.414378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la población de algunas :@0.741105:0.444447:0.903424:0.444447:0.903424:0.429507:0.741105:0.429507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bacterias puede llegar a :@0.741105:0.459576:0.903723:0.459576:0.903723:0.444636:0.741105:0.444636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
doblarse cada 15 minutos, :@0.741105:0.474705:0.919535:0.474705:0.919535:0.459765:0.741105:0.459765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 duplicaciones por hora :@0.741105:0.489833:0.909933:0.489833:0.909933:0.474894:0.741105:0.474894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y 96 diarias. Por ello, el aná-:@0.741105:0.504962:0.921363:0.504962:0.921363:0.490023:0.741105:0.490023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lisis del comportamiento :@0.741105:0.520091:0.910499:0.520091:0.910499:0.505152:0.741105:0.505152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de reproducción es im-:@0.741105:0.535220:0.895910:0.535220:0.895910:0.520280:0.741105:0.520280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
portante para controlar su :@0.741105:0.550349:0.918934:0.550349:0.918934:0.535409:0.741105:0.535409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expansión.:@0.741105:0.565478:0.812726:0.565478:0.812726:0.550538:0.741105:0.550538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga y escribe otras apli-:@0.741105:0.587756:0.918717:0.587756:0.918717:0.572816:0.741105:0.572816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
caciones de las sucesiones :@0.741105:0.602884:0.921296:0.602884:0.921296:0.587945:0.741105:0.587945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
numéricas en la vida diaria.:@0.741105:0.618013:0.920539:0.618013:0.920539:0.603074:0.741105:0.603074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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