198:
43:
893:
899:
904:
95:
223:
244:
1322:
1264:
1234:
1204:
945:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
234:
1371:
69:
65:
61:
57:
53:
47:
106:
78:
1321:
1316:
1288:
1263:
1258:
1233:
1228:
1149:
1079:
1043:
250:
1394:
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
952:
1133:
1027:
1099:
1063:
1010:
197:
914:
1397:
If the file has been modified from its original state, some details may not fully reflect the modified file.
1349:
The following pages on the
English Knowledge (XXG) use this file (pages on other projects are not listed):
1203:
1198:
42:
951:– If you remix, transform, or build upon the material, you must distribute your contributions under the
911:
1332:
1302:
1274:
1244:
1214:
114:
182:
394:= [rectangle, draw, fill=red!20, node distance=8cm, text centered, rounded corners]
383:= [rectangle, draw, fill=green!20, node distance=8cm, text centered, rounded corners]
101:
886:
I, the copyright holder of this work, hereby publish it under the following license:
361:= [diamond, draw, fill=yellow!20, aspect=2, text badly centered, inner sep=0pt]
158:
1353:
229:
372:= [rectangle, draw, fill=blue!20, text centered, rounded corners]
1171:
Click on a date/time to view the file as it appeared at that time.
1381:
89:
222:
1080:
Creative
Commons Attribution-ShareAlike 4.0 International
243:
83:(SVG file, nominally 478 × 551 pixels, file size: 51 KB)
1281:
Reverted to version as of 17:37, 15 November 2015 (UTC)
994:
Add a one-line explanation of what this file represents
133:
113:
Commons is a freely licensed media file repository.
178:
962:https://creativecommons.org/licenses/by-sa/4.0
94:
968:Creative Commons Attribution-Share Alike 4.0
892:
8:
928:– to copy, distribute and transmit the work
46:Size of this PNG preview of this SVG file:
1399:
1173:
990:
1364:The following other wikis use this file:
915:Attribution-Share Alike 4.0 International
1409:
1401:
1351:
1147:
1131:
1113:
1097:
1077:
1061:
1041:
1025:
1008:
1005:
986:
979:
193:
139:Decision diagram for the ratio test.svg
7:
249:This trigonometry was created with
1339:User created page with UploadWizard
1162:
903:
898:
149:Decision diagram for the ratio test
1392:
999:
993:
889:
885:
248:
227:
143:
126:
76:
998:
984:
939:Under the following conditions:
910:This file is licensed under the
902:
897:
891:
775:The ratio test cannot be applied
242:
221:
196:
93:
31:
21:
981:
144:
14:
980:
26:
1:
1150:original creation by uploader
36:
1006:Items portrayed in this file
1431:
1378:Usage on de.wikibooks.org
1368:Usage on ar.wikipedia.org
953:same or compatible license
1163:
168:
16:
983:
919:
267:
100:This is a file from the
1372:اختبار النسبة (رياضيات)
1338:
1317:17:37, 15 November 2015
1308:
1280:
1250:
1220:
783:(init) edge (case1);
189:
174:
164:
157:
154:
136:
104:. Information from its
1289:17:52, 10 January 2016
1259:17:53, 10 January 2016
1229:18:02, 10 January 2016
1221:Change \lim to \liminf
107:description page there
1382:Serlo: EN: Ratio test
685:converges absolutely
213:SVG development
70:1,777 × 2,048 pixels
934:– to adapt the work
52:Other resolutions:
1199:09:21, 7 June 2017
66:888 × 1,024 pixels
1418:
1417:
1360:Global file usage
1342:
1064:copyright license
992:
811:(case3) -- node
799:(case2) -- node
787:(case1) -- node
260:
259:
122:
121:
102:Wikimedia Commons
32:Global file usage
1422:
1400:
1329:
1299:
1271:
1241:
1211:
1115:15 November 2015
1028:copyright status
975:
972:
969:
966:
963:
955:as the original.
912:Creative Commons
906:
905:
901:
900:
895:
894:
875:
871:
868:
865:
861:
858:
854:
850:
847:(case3) -- node
846:
842:
838:
835:(case2) -- node
834:
830:
826:
823:(case1) -- node
822:
818:
814:
810:
806:
802:
798:
794:
790:
786:
782:
778:
774:
770:
766:
762:
759:
756:
753:
750:
747:
744:
741:
738:
735:
731:
727:
723:
720:
717:
714:
711:
708:
705:
702:
699:
696:
692:
688:
684:
681:
678:
675:
672:
669:
666:
663:
660:
657:
653:
649:
645:
642:
639:
636:
633:
629:
626:
623:
620:
617:
614:
611:
608:
605:
602:
599:
596:
593:
589:
585:
581:
577:
574:
571:
568:
565:
562:
559:
556:
553:
550:
547:
544:
541:
538:
535:
532:
528:
524:
520:
516:
513:
510:
507:
504:
501:
498:
495:
492:
489:
486:
483:
480:
477:
474:
471:
467:
463:
459:
456:
453:
450:
447:
444:
441:
438:
435:
432:
429:
426:
422:
418:
415:
411:
408:
404:
400:
397:
393:
389:
386:
382:
378:
375:
371:
367:
364:
360:
356:
353:
350:
346:
343:
340:
337:
334:
331:
328:
324:
321:
318:
314:
311:
308:
304:
301:
298:
294:
291:
288:
284:
281:
278:
274:
271:
246:
237:
225:
200:
170:
160:
159:15 November 2015
148:
140:
134:
118:
97:
96:
90:
84:
73:
62:666 × 768 pixels
58:416 × 480 pixels
54:208 × 240 pixels
48:478 × 551 pixels
1430:
1429:
1425:
1424:
1423:
1421:
1420:
1419:
1388:
1358:
1350:
1343:
1335:
1327:
1305:
1297:
1277:
1269:
1247:
1239:
1217:
1209:
1165:
1164:
1161:
1160:
1159:
1158:
1157:
1156:
1155:
1154:
1152:
1140:
1139:
1138:
1136:
1125:
1124:
1123:
1122:
1121:
1120:
1119:
1118:
1116:
1106:
1105:
1104:
1102:
1091:
1090:
1089:
1088:
1087:
1086:
1085:
1084:
1082:
1070:
1069:
1068:
1066:
1055:
1054:
1053:
1052:
1051:
1050:
1049:
1048:
1046:
1034:
1033:
1032:
1030:
1019:
1018:
1017:
1016:
1015:
1013:
997:
996:
995:
978:
977:
976:
973:
970:
967:
964:
961:
960:
918:
907:
888:
887:
882:
877:
876:
873:
869:
866:
863:
859:
856:
852:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
808:
804:
800:
796:
792:
788:
784:
780:
776:
772:
768:
764:
760:
757:
754:
751:
748:
745:
742:
739:
736:
733:
729:
725:
721:
718:
715:
712:
709:
706:
703:
700:
697:
694:
690:
686:
682:
679:
676:
673:
670:
667:
664:
661:
658:
655:
651:
647:
643:
640:
637:
634:
631:
630:for almost all
627:
624:
621:
618:
615:
612:
609:
606:
603:
600:
597:
594:
591:
587:
583:
579:
575:
572:
569:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
536:
533:
530:
526:
522:
518:
514:
511:
508:
505:
502:
499:
496:
493:
490:
487:
484:
481:
478:
475:
472:
469:
465:
461:
457:
454:
451:
448:
445:
442:
439:
436:
433:
430:
427:
424:
420:
416:
413:
409:
406:
402:
398:
395:
391:
387:
384:
380:
376:
373:
369:
365:
362:
358:
354:
351:
348:
344:
341:
338:
335:
332:
329:
326:
322:
320:\usetikzlibrary
319:
316:
312:
309:
306:
302:
299:
296:
292:
289:
286:
282:
279:
276:
272:
269:
266:
261:
256:
255:
254:
240:
239:
233:
216:
206:
205:
201:
150:
138:
131:
124:
123:
112:
111:
110:is shown below.
86:
82:
75:
74:
51:
12:
11:
5:
1428:
1426:
1416:
1415:
1412:
1408:
1407:
1404:
1391:
1387:
1386:
1385:
1384:
1376:
1375:
1374:
1362:
1361:
1357:
1356:
1348:
1347:
1346:
1341:
1340:
1337:
1333:
1330:
1324:
1319:
1314:
1311:
1310:
1307:
1303:
1300:
1294:
1291:
1286:
1283:
1282:
1279:
1275:
1272:
1266:
1261:
1256:
1253:
1252:
1249:
1245:
1242:
1236:
1231:
1226:
1223:
1222:
1219:
1215:
1212:
1206:
1201:
1196:
1192:
1191:
1188:
1185:
1182:
1179:
1176:
1169:
1168:
1153:
1148:
1146:
1145:
1144:
1143:
1142:
1141:
1137:
1134:source of file
1132:
1130:
1129:
1128:
1127:
1126:
1117:
1114:
1112:
1111:
1110:
1109:
1108:
1107:
1103:
1098:
1096:
1095:
1094:
1093:
1092:
1083:
1078:
1076:
1075:
1074:
1073:
1072:
1071:
1067:
1062:
1060:
1059:
1058:
1057:
1056:
1047:
1042:
1040:
1039:
1038:
1037:
1036:
1035:
1031:
1026:
1024:
1023:
1022:
1021:
1020:
1014:
1009:
1007:
1004:
1003:
1002:
1001:
1000:
989:
988:
985:
982:
959:
958:
957:
956:
946:
937:
936:
935:
929:
922:You are free:
909:
908:
890:
884:
883:
881:
878:
270:\documentclass
268:
265:
262:
258:
257:
241:
220:
219:
217:
214:
210:
209:
208:
207:
204:German version
203:
202:
195:
191:
190:Other versions
187:
186:
176:
172:
171:
166:
162:
161:
156:
152:
151:
141:
132:
130:
127:
125:
120:
119:
98:
88:
87:
45:
41:
40:
39:
34:
29:
24:
19:
13:
10:
9:
6:
4:
3:
2:
1427:
1413:
1410:
1405:
1402:
1398:
1395:
1389:
1383:
1380:
1379:
1377:
1373:
1370:
1369:
1367:
1366:
1365:
1359:
1355:
1352:
1344:
1336:
1334:Stephan Kulla
1331:
1325:
1323:
1320:
1318:
1315:
1313:
1312:
1306:
1304:Stephan Kulla
1301:
1295:
1292:
1290:
1287:
1285:
1284:
1278:
1276:Stephan Kulla
1273:
1267:
1265:
1262:
1260:
1257:
1255:
1254:
1248:
1246:Stephan Kulla
1243:
1237:
1235:
1232:
1230:
1227:
1225:
1224:
1218:
1216:Stephan Kulla
1213:
1207:
1205:
1202:
1200:
1197:
1194:
1193:
1189:
1186:
1183:
1180:
1177:
1175:
1174:
1172:
1166:
1151:
1135:
1101:
1081:
1065:
1045:
1029:
1012:
965:CC BY-SA 4.0
954:
950:
947:
944:
941:
940:
938:
933:
930:
927:
924:
923:
921:
920:
916:
913:
896:
879:
336:\displaystyle
325:shapes,arrows
263:
252:
245:
236:
231:
224:
218:
212:
211:
199:
194:
192:
188:
184:
183:Stephan Kulla
180:
179:Stephan Kulla
177:
173:
167:
163:
153:
147:
142:
135:
128:
116:
109:
108:
103:
99:
92:
91:
85:
80:
79:Original file
71:
67:
63:
59:
55:
49:
44:
38:
35:
33:
30:
28:
25:
23:
20:
18:
15:
1396:
1393:
1363:
1293:No thumbnail
1170:
1167:File history
948:
942:
931:
925:
145:
115:You can help
105:
77:
22:File history
1044:copyrighted
949:share alike
943:attribution
862:tikzpicture
843:(case3);
831:(case2);
412:tikzpicture
379:convergence
310:\usepackage
300:\usepackage
290:\usepackage
280:\usepackage
264:Source code
137:Description
1354:Ratio test
1345:File usage
1326:478 × 551
1268:478 × 551
1238:478 × 551
1208:478 × 551
1184:Dimensions
795:(yes1);
638:\in\mathbb
423:Calculate
396:\tikzstyle
390:divergence
385:\tikzstyle
374:\tikzstyle
363:\tikzstyle
352:\tikzstyle
330:\everymath
275:standalone
27:File usage
1414:440.431pt
1406:382.181pt
1181:Thumbnail
1178:Date/Time
1100:inception
880:Licensing
855:(final);
819:(no3);
807:(no2);
540:\to\infty
479:\to\infty
215:InfoField
146:English:
1390:Metadata
987:Captions
932:to remix
926:to share
917:license.
872:document
771:(final)
763:diverges
724:diverges
586:(case3)
525:(case2)
464:(case1)
357:decision
347:document
285:inputenc
232:code is
169:Own work
37:Metadata
1328:(51 KB)
1298:(14 KB)
1270:(51 KB)
1240:(51 KB)
1210:(51 KB)
1195:current
1190:Comment
1011:depicts
991:English
654:(yes1)
613:}}{a_k}
570:| >
564:}}{a_k}
534:\liminf
509:| <
503:}}{a_k}
473:\limsup
446:}}{a_k}
419:(init)
305:amssymb
295:amsmath
251:dvisvgm
129:Summary
81:
1411:Height
1296:0 × 0
755:\infty
732:(no3)
716:\infty
693:(no2)
677:\infty
616:\right
567:\right
506:\right
449:\right
407:\begin
342:\begin
247:
226:
175:Author
165:Source
1403:Width
845:\path
833:\path
821:\path
809:\path
797:\path
785:\path
781:\path
769:\node
730:\node
691:\node
652:\node
604:{a_{k
601:\frac
595:\left
584:\node
555:{a_{k
552:\frac
546:\left
523:\node
494:{a_{k
491:\frac
485:\left
462:\node
437:{a_{k
434:\frac
428:\left
417:\node
368:block
235:valid
1309:typo
1251:typo
1187:User
974:true
971:true
867:\end
857:\end
779:;
767:;
740:\sum
728:;
701:\sum
689:;
662:\sum
650:;
582:;
521:;
460:;
401:line
315:tikz
228:The
155:Date
17:File
815:Yes
803:Yes
791:Yes
758:a_k
743:_{k
719:a_k
704:_{k
680:a_k
665:_{k
622:\ge
590:Is
537:_{k
529:Is
476:_{k
468:Is
405:=
230:SVG
851:No
839:No
827:No
761:$
752:}^
737:$
722:$
713:}^
698:$
683:$
674:}^
659:$
644:$
632:$
628:$
619:|
592:$
576:$
543:}
531:$
515:$
482:}
470:$
455:$
425:$
68:|
64:|
60:|
56:|
50:.
874:}
870:{
864:}
860:{
853:}
849:{
841:}
837:{
829:}
825:{
817:}
813:{
805:}
801:{
793:}
789:{
777:}
773:{
765:}
749:1
746:=
734:{
726:}
710:1
707:=
695:{
687:}
671:1
668:=
656:{
648:}
646:?
641:N
635:k
625:1
610:1
607:+
598:|
588:{
580:}
578:?
573:1
561:1
558:+
549:|
527:{
519:}
517:?
512:1
500:1
497:+
488:|
466:{
458:}
452:|
443:1
440:+
431:|
421:{
414:}
410:{
403:}
399:{
392:}
388:{
381:}
377:{
370:}
366:{
359:}
355:{
349:}
345:{
339:}
333:{
327:}
323:{
317:}
313:{
307:}
303:{
297:}
293:{
287:}
283:{
277:}
273:{
253:.
238:.
185:)
181:(
117:.
72:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.