112:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000 Definición :@0.404236:0.167937:0.491103:0.167937:0.491103:0.150991:0.404236:0.150991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sea , ≠ Ø. Se llama sucesión numérica real a toda :@0.484322:0.167474:0.895904:0.167474:0.895904:0.150977:0.484322:0.150977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.519746:0.175061:0.525333:0.175061:0.525333:0.156062:0.519746:0.156062:0.000000:0.000000 :@0.529666:0.167257:0.545714:0.167257:0.545714:0.152611:0.529666:0.152611:0.000000 N:@0.550051:0.166387:0.564387:0.166387:0.564387:0.153525:0.550051:0.153525:0.000000 :@0.571479:0.175061:0.577066:0.175061:0.577066:0.156062:0.571479:0.156062:0.000000:0.000000 función de en .:@0.404235:0.184825:0.544381:0.184825:0.544381:0.168327:0.404235:0.168327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.463360:0.184941:0.472338:0.184941:0.472338:0.168472:0.463360:0.168472:0.000000 I:@0.498479:0.184941:0.502486:0.184941:0.502486:0.168472:0.498479:0.168472:0.000000 R:@0.528321:0.183738:0.541626:0.183738:0.541626:0.170876:0.528321:0.170876:0.000000 Notaciones:@0.404236:0.220924:0.495222:0.220924:0.495222:0.203241:0.404236:0.203241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si es una sucesión, es la función ( )::@0.404236:0.237632:0.690150:0.237632:0.690150:0.221134:0.404236:0.221134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.420188:0.237747:0.429165:0.237747:0.429165:0.221279:0.420188:0.221279:0.000000 a:@0.550592:0.237747:0.559570:0.237747:0.559570:0.221279:0.550592:0.221279:0.000000 a n:@0.657148:0.237747:0.681442:0.237747:0.681442:0.221279:0.657148:0.221279:0.000000:0.000000:0.000000 El conjunto se llama conjunto de índices y :@0.404236:0.265668:0.716226:0.265675:0.716226:0.249177:0.404236:0.249170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.489690:0.273261:0.495277:0.273261:0.495277:0.254262:0.489690:0.254262:0.000000:0.000000 n :@0.716092:0.265790:0.729597:0.265790:0.729597:0.249322:0.716092:0.249322:0.000000:0.000000 :@0.729446:0.265458:0.745494:0.265458:0.745494:0.250811:0.729446:0.250811:0.000000 se dice índice de la :@0.745880:0.265675:0.895926:0.265675:0.895926:0.249177:0.745880:0.249177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.749878:0.273261:0.755466:0.273261:0.755466:0.254262:0.749878:0.254262:0.000000:0.000000 sucesión. Para cada :@0.404240:0.283025:0.545297:0.283025:0.545297:0.266528:0.404240:0.266528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n :@0.545894:0.283141:0.559399:0.283141:0.559399:0.266672:0.545894:0.266672:0.000000:0.000000 :@0.560000:0.282808:0.576048:0.282808:0.576048:0.268162:0.560000:0.268162:0.000000 , el número real ( ) se denomina término :@0.576433:0.283025:0.895917:0.283025:0.895917:0.266528:0.576433:0.266528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.581163:0.290612:0.586751:0.290612:0.586751:0.271613:0.581163:0.271613:0.000000:0.000000 a n:@0.702186:0.283141:0.726479:0.283141:0.726479:0.266672:0.702186:0.266672:0.000000:0.000000:0.000000 general de la sucesión y se denota como , es decir que ( ) = . A :@0.404231:0.300376:0.895911:0.300376:0.895911:0.283878:0.404231:0.283878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.696736:0.300492:0.705713:0.300492:0.705713:0.284023:0.696736:0.284023:0.000000 n:@0.705567:0.303722:0.711025:0.303722:0.711025:0.294120:0.705567:0.294120:0.000000 a n:@0.808447:0.300492:0.832741:0.300492:0.832741:0.284023:0.808447:0.284023:0.000000:0.000000:0.000000 a:@0.858404:0.300492:0.867381:0.300492:0.867381:0.284023:0.858404:0.284023:0.000000 n:@0.867229:0.303722:0.872687:0.303722:0.872687:0.294120:0.867229:0.294120:0.000000 la sucesión real se la denota ( ) o simplemente ( ), siempre que :@0.404233:0.317727:0.895897:0.317727:0.895897:0.301229:0.404233:0.301229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.512889:0.317843:0.521866:0.317843:0.521866:0.301374:0.512889:0.301374:0.000000 a:@0.619830:0.317843:0.628808:0.317843:0.628808:0.301374:0.619830:0.301374:0.000000 n n:@0.628710:0.321072:0.645580:0.321072:0.645580:0.311471:0.628710:0.311471:0.000000:0.000000:0.000000 :@0.645581:0.320912:0.654124:0.320912:0.654124:0.313116:0.645581:0.313116:0.000000 :@0.654328:0.325082:0.658029:0.325082:0.658029:0.315012:0.654328:0.315012:0.000000:0.000000 a:@0.778255:0.317843:0.787233:0.317843:0.787233:0.301374:0.778255:0.301374:0.000000 n:@0.787100:0.321072:0.792559:0.321072:0.792559:0.311471:0.787100:0.311471:0.000000 no haya peligro de confusión. Se dirá sucesión ( ) o también suce-:@0.404229:0.335078:0.891754:0.335078:0.891754:0.318580:0.404229:0.318580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.748840:0.335193:0.757817:0.335193:0.757817:0.318725:0.748840:0.318725:0.000000 n:@0.757720:0.338423:0.763179:0.338423:0.763179:0.328822:0.757720:0.328822:0.000000 sión real; su término general es . El conjunto { | :@0.404228:0.352428:0.809474:0.352428:0.809474:0.335931:0.404228:0.335931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.627801:0.352544:0.636779:0.352544:0.636779:0.336075:0.627801:0.336075:0.000000 n:@0.636647:0.355774:0.642106:0.355774:0.642106:0.346173:0.636647:0.346173:0.000000 a:@0.742036:0.352544:0.751013:0.352544:0.751013:0.336075:0.742036:0.336075:0.000000 n:@0.750865:0.355774:0.756324:0.355774:0.756324:0.346173:0.750865:0.346173:0.000000 :@0.760948:0.352211:0.776996:0.352211:0.776996:0.337565:0.760948:0.337565:0.000000 R:@0.782395:0.351341:0.795699:0.351341:0.795699:0.338479:0.782395:0.338479:0.000000 n :@0.809956:0.352544:0.823461:0.352544:0.823461:0.336075:0.809956:0.336075:0.000000:0.000000 :@0.823942:0.352211:0.839990:0.352211:0.839990:0.337565:0.823942:0.337565:0.000000 } es el :@0.840376:0.352428:0.895907:0.352428:0.895907:0.335931:0.840376:0.335931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.845010:0.360015:0.850597:0.360015:0.850597:0.341016:0.845010:0.341016:0.000000:0.000000 recorrido de la sucesión ( ). Este conjunto puede ser finito.:@0.404239:0.369779:0.826568:0.369779:0.826568:0.353281:0.404239:0.353281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.582710:0.369895:0.591688:0.369895:0.591688:0.353426:0.582710:0.353426:0.000000 n:@0.591530:0.373125:0.596988:0.373125:0.596988:0.363523:0.591530:0.363523:0.000000 El conjunto {(:@0.404239:0.404481:0.503243:0.404481:0.503243:0.387983:0.404239:0.387983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n, a:@0.503243:0.404596:0.529000:0.404596:0.529000:0.388128:0.503243:0.388128:0.000000:0.000000:0.000000:0.000000 n:@0.528846:0.407826:0.534304:0.407826:0.534304:0.398225:0.528846:0.398225:0.000000 ) :@0.534303:0.404481:0.566091:0.404481:0.566091:0.387983:0.534303:0.387983:0.000000:0.000000:0.000000:0.000000 :@0.545516:0.404264:0.561564:0.404264:0.561564:0.389617:0.545516:0.389617:0.000000 R:@0.567210:0.403394:0.580515:0.403394:0.580515:0.390532:0.567210:0.390532:0.000000 2:@0.580515:0.398129:0.585468:0.398129:0.585468:0.388511:0.580515:0.388511:0.000000 | :@0.585467:0.404481:0.599492:0.404481:0.599492:0.387983:0.585467:0.387983:0.000000:0.000000:0.000000 n :@0.600224:0.404596:0.613729:0.404596:0.613729:0.388128:0.600224:0.388128:0.000000:0.000000 :@0.614461:0.404264:0.630509:0.404264:0.630509:0.389617:0.614461:0.389617:0.000000 } se llama grafo de la sucesión. Este :@0.630894:0.404481:0.895910:0.404481:0.895910:0.387983:0.630894:0.387983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.635773:0.412067:0.641360:0.412067:0.641360:0.393068:0.635773:0.393068:0.000000:0.000000 conjunto se representa gráficamente en el sistema de coordenadas :@0.404241:0.421831:0.895867:0.421831:0.895867:0.405334:0.404241:0.405334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 rectangulares y, al resultado de esa gráfica, se lo denomina gráfica de :@0.404241:0.439182:0.895956:0.439182:0.895956:0.422684:0.404241:0.422684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la sucesión ( ).:@0.404241:0.456533:0.514053:0.456533:0.514053:0.440035:0.404241:0.440035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.491068:0.456649:0.500045:0.456649:0.500045:0.440180:0.491068:0.440180:0.000000 n:@0.499886:0.459878:0.505344:0.459878:0.505344:0.450277:0.499886:0.450277:0.000000 Definición :@0.404241:0.491697:0.491108:0.491697:0.491108:0.474751:0.404241:0.474751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Una sucesión ( ) se dice finita si el conjunto de índi-:@0.484327:0.491234:0.891699:0.491234:0.891699:0.474737:0.484327:0.474737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.595430:0.491350:0.604407:0.491350:0.604407:0.474881:0.595430:0.474881:0.000000 n n:@0.604256:0.494580:0.621125:0.494580:0.621125:0.484979:0.604256:0.484979:0.000000:0.000000:0.000000 :@0.621126:0.494420:0.629668:0.494420:0.629668:0.486623:0.621126:0.486623:0.000000 :@0.629873:0.498589:0.633574:0.498589:0.633574:0.488520:0.629873:0.488520:0.000000:0.000000 I:@0.829433:0.491350:0.833441:0.491350:0.833441:0.474881:0.829433:0.474881:0.000000 ces es finito. En el caso contrario, la sucesión se dice infinita. :@0.404232:0.508585:0.829969:0.508585:0.829969:0.492087:0.404232:0.492087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404232:0.525936:0.412516:0.525936:0.412516:0.509438:0.404232:0.509438:0.000000:0.000000 No se debe confundir una sucesión finita ( es finito) con una sucesión :@0.404232:0.543287:0.895919:0.543287:0.895919:0.526789:0.404232:0.526789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.697494:0.550873:0.703081:0.550873:0.703081:0.531874:0.697494:0.531874:0.000000:0.000000 que toma un número finito de valores, o sea, que su recorrido es finito.:@0.404235:0.560637:0.872179:0.560637:0.872179:0.544140:0.404235:0.544140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideremos el siguiente ejemplo: ( ) la sucesión real definida:@0.404235:0.595339:0.856373:0.595339:0.856373:0.578841:0.404235:0.578841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.663927:0.595455:0.672905:0.595455:0.672905:0.578986:0.663927:0.578986:0.000000 n:@0.672752:0.598684:0.678211:0.598684:0.678211:0.589083:0.672752:0.589083:0.000000 como: = , :@0.404239:0.621596:0.555319:0.621600:0.555319:0.605103:0.404239:0.605099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.452922:0.621712:0.461900:0.621712:0.461900:0.605243:0.452922:0.605243:0.000000 n:@0.461742:0.624944:0.467201:0.624944:0.467201:0.615343:0.461742:0.615343:0.000000 n :@0.555319:0.621716:0.568824:0.621716:0.568824:0.605247:0.555319:0.605247:0.000000:0.000000 :@0.568824:0.621383:0.584872:0.621383:0.584872:0.606736:0.568824:0.606736:0.000000 . Si se escribe = , :@0.585258:0.621600:0.794469:0.621600:0.794469:0.605103:0.585258:0.605103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 N:@0.589397:0.620513:0.603734:0.620513:0.603734:0.607651:0.589397:0.607651:0.000000 a:@0.699343:0.621716:0.708321:0.621716:0.708321:0.605247:0.699343:0.605247:0.000000 j:@0.708245:0.624944:0.710492:0.624944:0.710492:0.615343:0.708245:0.615343:0.000000 j :@0.794469:0.621716:0.802464:0.621716:0.802464:0.605247:0.794469:0.605247:0.000000:0.000000 :@0.802464:0.621383:0.818512:0.621383:0.818512:0.606736:0.802464:0.606736:0.000000 , :@0.818897:0.621600:0.844271:0.621600:0.844271:0.605103:0.818897:0.605103:0.000000:0.000000:0.000000:0.000000 N:@0.823038:0.620513:0.837374:0.620513:0.837374:0.607651:0.823038:0.607651:0.000000 a:@0.404234:0.655102:0.413211:0.655102:0.413211:0.638633:0.404234:0.638633:0.000000 k:@0.413098:0.658333:0.417905:0.658333:0.417905:0.648732:0.413098:0.648732:0.000000 = , :@0.417904:0.654989:0.497740:0.654989:0.497740:0.638491:0.417904:0.638491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k :@0.497740:0.655105:0.510127:0.655105:0.510127:0.638636:0.497740:0.638636:0.000000:0.000000 :@0.510127:0.654772:0.526175:0.654772:0.526175:0.640125:0.510127:0.640125:0.000000 , = , :@0.526561:0.654989:0.650137:0.654989:0.650137:0.638491:0.526561:0.638491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 N:@0.530702:0.653902:0.545038:0.653902:0.545038:0.641040:0.530702:0.641040:0.000000 a:@0.551935:0.655105:0.560913:0.655105:0.560913:0.638636:0.551935:0.638636:0.000000 p:@0.560757:0.658333:0.566160:0.658333:0.566160:0.648732:0.560757:0.648732:0.000000 p :@0.650137:0.655105:0.663546:0.655105:0.663546:0.638636:0.650137:0.638636:0.000000:0.000000 :@0.663546:0.654772:0.679594:0.654772:0.679594:0.640125:0.663546:0.640125:0.000000 :@0.679979:0.654989:0.684121:0.654989:0.684121:0.638491:0.679979:0.638491:0.000000 N:@0.684118:0.653902:0.698455:0.653902:0.698455:0.641040:0.684118:0.641040:0.000000 , :@0.698455:0.655105:0.705448:0.655105:0.705448:0.638636:0.698455:0.638636:0.000000:0.000000 todas representan el:@0.705448:0.654989:0.849437:0.654989:0.849437:0.638491:0.705448:0.638491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mismo término general de la sucesión ( ) y se han utilizado tres tipos :@0.404236:0.683025:0.895861:0.683032:0.895861:0.666534:0.404236:0.666527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.678880:0.683141:0.687857:0.683141:0.687857:0.666672:0.678880:0.666672:0.000000 n:@0.687754:0.686376:0.693212:0.686376:0.693212:0.676775:0.687754:0.676775:0.000000 de índices , , del conjunto de índices de la sucesión ( ).:@0.404235:0.700383:0.839537:0.700383:0.839537:0.683885:0.404235:0.683885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j k p:@0.479521:0.700498:0.514680:0.700498:0.514680:0.684030:0.479521:0.684030:0.000000:0.000000:0.000000:0.000000:0.000000 N:@0.689241:0.699296:0.703578:0.699296:0.703578:0.686434:0.689241:0.686434:0.000000 a:@0.816548:0.700498:0.825525:0.700498:0.825525:0.684030:0.816548:0.684030:0.000000 n:@0.825370:0.703727:0.830828:0.703727:0.830828:0.694126:0.825370:0.694126:0.000000 Definición :@0.404239:0.735547:0.491106:0.735547:0.491106:0.718601:0.404239:0.718601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean , con ≠ Ø. Diremos que las sucesiones reales :@0.484324:0.735084:0.895950:0.735084:0.895950:0.718586:0.484324:0.718586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.528775:0.742671:0.534362:0.742671:0.534362:0.723672:0.528775:0.723672:0.000000:0.000000 :@0.538446:0.734867:0.554494:0.734867:0.554494:0.720220:0.538446:0.720220:0.000000 N:@0.558568:0.733997:0.572904:0.733997:0.572904:0.721135:0.558568:0.721135:0.000000 :@0.610770:0.742671:0.616357:0.742671:0.616357:0.723672:0.610770:0.723672:0.000000:0.000000 ( ) y ( ) son iguales y escribimos ( ) = ( ) si y solo si:@0.404245:0.752435:0.859090:0.752435:0.859090:0.735937:0.404245:0.735937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.410198:0.752551:0.419175:0.752551:0.419175:0.736082:0.410198:0.736082:0.000000 j j:@0.419089:0.755779:0.429534:0.755779:0.429534:0.746178:0.419089:0.746178:0.000000:0.000000:0.000000 :@0.429534:0.755619:0.438076:0.755619:0.438076:0.747823:0.429534:0.747823:0.000000 :@0.438282:0.759790:0.441984:0.759790:0.441984:0.749720:0.438282:0.749720:0.000000:0.000000 b:@0.464822:0.752551:0.474089:0.752551:0.474089:0.736082:0.464822:0.736082:0.000000 n n:@0.474032:0.755779:0.490900:0.755779:0.490900:0.746178:0.474032:0.746178:0.000000:0.000000:0.000000 :@0.490901:0.755619:0.499444:0.755619:0.499444:0.747823:0.490901:0.747823:0.000000 :@0.499648:0.759790:0.503349:0.759790:0.503349:0.749720:0.499648:0.749720:0.000000:0.000000 a:@0.688091:0.752551:0.697068:0.752551:0.697068:0.736082:0.688091:0.736082:0.000000 j j:@0.696989:0.755779:0.707436:0.755779:0.707436:0.746178:0.696989:0.746178:0.000000:0.000000:0.000000 :@0.707434:0.755619:0.715977:0.755619:0.715977:0.747823:0.707434:0.747823:0.000000 :@0.716183:0.759790:0.719884:0.759790:0.719884:0.749720:0.716183:0.749720:0.000000:0.000000 b:@0.745709:0.752551:0.754975:0.752551:0.754975:0.736082:0.745709:0.736082:0.000000 n n:@0.754917:0.755779:0.771788:0.755779:0.771788:0.746178:0.754917:0.746178:0.000000:0.000000:0.000000 :@0.771787:0.755619:0.780330:0.755619:0.780330:0.747823:0.771787:0.747823:0.000000 :@0.780535:0.759790:0.784237:0.759790:0.784237:0.749720:0.780535:0.749720:0.000000:0.000000 a:@0.404239:0.777030:0.413216:0.777030:0.413216:0.760561:0.404239:0.760561:0.000000 j:@0.413137:0.780259:0.415383:0.780259:0.415383:0.770657:0.413137:0.770657:0.000000 = :@0.415383:0.776913:0.434475:0.776913:0.434475:0.760416:0.415383:0.760416:0.000000:0.000000:0.000000 b , j, n:@0.434475:0.777029:0.490178:0.777029:0.490178:0.760560:0.434475:0.760560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.443683:0.780259:0.449142:0.780259:0.449142:0.770657:0.443683:0.770657:0.000000 ∀:@0.458350:0.784500:0.469922:0.784500:0.469922:0.765501:0.458350:0.765501:0.000000 .:@0.490178:0.776913:0.521455:0.776913:0.521455:0.760416:0.490178:0.760416:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.494319:0.776395:0.508971:0.776395:0.508971:0.763021:0.494319:0.763021:0.000000 :@0.513113:0.784500:0.518701:0.784500:0.518701:0.765501:0.513113:0.765501:0.000000:0.000000 Ejercicio resuelto:@0.404245:0.811991:0.522224:0.811991:0.522224:0.795204:0.404245:0.795204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideremos la sucesión ( ) definida como = , .:@0.404245:0.828966:0.850445:0.828966:0.850445:0.812468:0.404245:0.812468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.597050:0.829081:0.606028:0.829081:0.606028:0.812612:0.597050:0.812612:0.000000 n:@0.605863:0.832310:0.611322:0.832310:0.611322:0.822708:0.605863:0.822708:0.000000 a :@0.729511:0.829081:0.747936:0.829081:0.747936:0.812612:0.729511:0.812612:0.000000:0.000000:0.000000 n:@0.738336:0.832310:0.743795:0.832310:0.743795:0.822708:0.738336:0.822708:0.000000 n:@0.794635:0.829081:0.803998:0.829081:0.803998:0.812612:0.794635:0.812612:0.000000 :@0.808140:0.828749:0.824188:0.828749:0.824188:0.814102:0.808140:0.814102:0.000000 Z:@0.829099:0.827879:0.841390:0.827879:0.841390:0.815016:0.829099:0.815016:0.000000 +:@0.841390:0.820099:0.847691:0.820099:0.847691:0.810481:0.841390:0.810481:0.000000 El término general de esta sucesión está definido como:@0.404243:0.853445:0.795283:0.853445:0.795283:0.836947:0.404243:0.836947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a :@0.404243:0.878039:0.422660:0.878039:0.422660:0.861571:0.404243:0.861571:0.000000:0.000000:0.000000 n:@0.413060:0.881268:0.418518:0.881268:0.418518:0.871667:0.413060:0.871667:0.000000 = , . Nota que el conjunto en el que está definida:@0.422660:0.877924:0.845718:0.877924:0.845718:0.861426:0.422660:0.861426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.469359:0.878039:0.478722:0.878039:0.478722:0.861571:0.469359:0.861571:0.000000 :@0.482864:0.877707:0.498912:0.877707:0.498912:0.863060:0.482864:0.863060:0.000000 Z:@0.503822:0.876837:0.516114:0.876837:0.516114:0.863974:0.503822:0.863974:0.000000 +:@0.516114:0.869056:0.522415:0.869056:0.522415:0.859438:0.516114:0.859438:0.000000 la sucesión es :@0.404241:0.902403:0.503629:0.902403:0.503629:0.885905:0.404241:0.885905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.503623:0.909988:0.509210:0.909988:0.509210:0.890989:0.503623:0.890989:0.000000:0.000000 =:@0.509210:0.902518:0.524237:0.902518:0.524237:0.886049:0.509210:0.886049:0.000000:0.000000 .:@0.524237:0.902402:0.549725:0.902402:0.549725:0.885904:0.524237:0.885904:0.000000:0.000000:0.000000 Z:@0.528378:0.901315:0.540669:0.901315:0.540669:0.888453:0.528378:0.888453:0.000000 +:@0.540669:0.893534:0.546970:0.893534:0.546970:0.883916:0.540669:0.883916:0.000000 M.5.1.53. Identificar sucesiones numéricas reales, sucesiones monótonas y sucesiones definidas por recurrencia a partir de las fórmulas que las definen.:@0.143847:0.940354:0.754830:0.940354:0.754830:0.930312:0.143847:0.930312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición de sucesión numérica real:@0.404235:0.127666:0.853634:0.127666:0.853634:0.083007:0.404235:0.083007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.710328:0.242233:0.715915:0.242233:0.715915:0.223234:0.710328:0.223234:0.000000:0.000000 ,:@0.715915:0.234647:0.756399:0.234647:0.756399:0.218149:0.715915:0.218149:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.720057:0.242746:0.736201:0.242746:0.736201:0.222883:0.720057:0.222883:0.000000 R:@0.740340:0.233560:0.753644:0.233560:0.753644:0.220698:0.740340:0.220698:0.000000 n:@0.710336:0.252113:0.719699:0.252113:0.719699:0.235645:0.710336:0.235645:0.000000 ( ).:@0.719699:0.251998:0.777129:0.251998:0.777129:0.235500:0.719699:0.235500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.723841:0.260097:0.739985:0.260097:0.739985:0.240234:0.723841:0.240234:0.000000 a n:@0.744127:0.252113:0.768421:0.252113:0.768421:0.235645:0.744127:0.235645:0.000000:0.000000:0.000000 n:@0.488353:0.613814:0.501858:0.613814:0.501858:0.597345:0.488353:0.597345:0.000000:0.000000 + 1:@0.501858:0.613698:0.529542:0.613698:0.529542:0.597200:0.501858:0.597200:0.000000:0.000000:0.000000:0.000000 n:@0.488045:0.630152:0.497408:0.630152:0.497408:0.613684:0.488045:0.613684:0.000000 2:@0.497406:0.623690:0.502359:0.623690:0.502359:0.614072:0.497406:0.614072:0.000000 + 1:@0.502360:0.630043:0.529948:0.630043:0.529948:0.613545:0.502360:0.613545:0.000000:0.000000:0.000000:0.000000 j:@0.736867:0.613814:0.744862:0.613814:0.744862:0.597345:0.736867:0.597345:0.000000:0.000000 + 1:@0.744862:0.613698:0.772546:0.613698:0.772546:0.597200:0.744862:0.597200:0.000000:0.000000:0.000000:0.000000 j:@0.736559:0.630152:0.740412:0.630152:0.740412:0.613684:0.736559:0.613684:0.000000 2:@0.740412:0.623690:0.745365:0.623690:0.745365:0.614072:0.740412:0.614072:0.000000 + 1:@0.745364:0.630043:0.772951:0.630043:0.772951:0.613545:0.745364:0.613545:0.000000:0.000000:0.000000:0.000000 k:@0.443768:0.647758:0.456156:0.647758:0.456156:0.631290:0.443768:0.631290:0.000000:0.000000 + 1:@0.456156:0.647643:0.483840:0.647643:0.483840:0.631145:0.456156:0.631145:0.000000:0.000000:0.000000:0.000000 k:@0.443460:0.664097:0.451706:0.664097:0.451706:0.647628:0.443460:0.647628:0.000000 2:@0.451704:0.657635:0.456657:0.657635:0.456657:0.648016:0.451704:0.648016:0.000000 + 1:@0.456658:0.663988:0.484246:0.663988:0.484246:0.647490:0.456658:0.647490:0.000000:0.000000:0.000000:0.000000 p:@0.591377:0.647758:0.604786:0.647758:0.604786:0.631290:0.591377:0.631290:0.000000:0.000000 + 1:@0.604786:0.647643:0.632470:0.647643:0.632470:0.631145:0.604786:0.631145:0.000000:0.000000:0.000000:0.000000 p:@0.591069:0.664097:0.600336:0.664097:0.600336:0.647628:0.591069:0.647628:0.000000 2:@0.600335:0.657635:0.605288:0.657635:0.605288:0.648016:0.600335:0.648016:0.000000 + 1:@0.605288:0.663988:0.632876:0.663988:0.632876:0.647490:0.605288:0.647490:0.000000:0.000000:0.000000:0.000000 1:@0.767457:0.820577:0.775953:0.820577:0.775953:0.804079:0.767457:0.804079:0.000000 n:@0.767033:0.837031:0.776396:0.837031:0.776396:0.820562:0.767033:0.820562:0.000000 1:@0.442316:0.870975:0.450812:0.870975:0.450812:0.854477:0.442316:0.854477:0.000000 n:@0.441892:0.887429:0.451255:0.887429:0.451255:0.870960:0.441892:0.870960:0.000000 Saberes previos:@0.199646:0.108582:0.307805:0.108582:0.307805:0.093110:0.199646:0.093110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Cuál es el conjunto de :@0.199884:0.137210:0.352934:0.137210:0.352934:0.122147:0.199884:0.122147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los números naturales?:@0.153341:0.153052:0.300655:0.153052:0.300655:0.137989:0.153341:0.137989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Desequilibrio cognitivo:@0.199646:0.196629:0.363493:0.196629:0.363493:0.181156:0.199646:0.181156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Cómo se expresa el tér-:@0.199884:0.225256:0.356593:0.225256:0.356593:0.210193:0.199884:0.210193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mino general de una sucesión?:@0.153341:0.241098:0.351526:0.241098:0.351526:0.226035:0.153341:0.226035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.199644:0.690036:0.297267:0.690036:0.297267:0.674564:0.199644:0.674564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 comunicacional:@0.199644:0.702604:0.311603:0.702604:0.311603:0.687132:0.199644:0.687132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aprende la siguiente :@0.193071:0.727078:0.329536:0.727078:0.329536:0.712015:0.193071:0.712015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 simbología matemática::@0.153335:0.742920:0.308107:0.742920:0.308107:0.727857:0.153335:0.727857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.153335:0.765996:0.161532:0.765996:0.161532:0.750959:0.153335:0.750959:0.000000 n:@0.161400:0.768944:0.166384:0.768944:0.166384:0.760178:0.161400:0.760178:0.000000 : sucesión real:@0.166384:0.765891:0.254948:0.765891:0.254948:0.750827:0.166384:0.750827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 N:@0.153350:0.787977:0.167035:0.787977:0.167035:0.775699:0.153350:0.775699:0.000000 : el conjunto de los números :@0.167123:0.788861:0.354755:0.788861:0.354755:0.773798:0.167123:0.773798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 naturales:@0.153350:0.804703:0.212134:0.804703:0.212134:0.789640:0.153350:0.789640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.153350:0.826790:0.166050:0.826790:0.166050:0.814512:0.153350:0.814512:0.000000 : el conjunto de los números :@0.166138:0.827674:0.353769:0.827674:0.353769:0.812611:0.166138:0.812611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 reales:@0.153350:0.843516:0.189409:0.843516:0.189409:0.828453:0.153350:0.828453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.199644:0.355051:0.297267:0.355051:0.297267:0.339579:0.199644:0.339579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.199644:0.367619:0.283707:0.367619:0.283707:0.352147:0.199644:0.352147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las sucesiones reales :@0.199880:0.392094:0.336729:0.392094:0.336729:0.377031:0.199880:0.377031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 convergentes son una clase de :@0.153337:0.407936:0.357448:0.407936:0.357448:0.392873:0.153337:0.392873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones cuyo conjunto de :@0.153337:0.423778:0.339295:0.423778:0.339295:0.408715:0.153337:0.408715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 salida es un subconjunto de los :@0.153337:0.439620:0.360052:0.439620:0.360052:0.424557:0.153337:0.424557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números naturales y el conjun-:@0.153337:0.455462:0.353580:0.455462:0.353580:0.440399:0.153337:0.440399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 to de llegada es el conjunto de :@0.153337:0.471304:0.355566:0.471304:0.355566:0.456241:0.153337:0.456241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los números reales.:@0.153337:0.487146:0.275463:0.487146:0.275463:0.472083:0.153337:0.472083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000