SeriesTestsSummary - Summary of Convergence _and Divergence...

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Unformatted text preview: Summary of Convergence _and Divergence Tests fer Series TEST SERIES Diverges if limb," a sf 0 Fl nth-{em Ea” ' Geemetrie Series Diverges if r .21 or r S —l Converge-s if — l a: r <1 Diverges if p E l P" . ~ . series _ Converge-s 11' p>l Diverges if _ f f{x}dx diverges Cenverges if I: fix) cunverges Divergcs: an 2 b” for every n: if Zia-n diverges. then Zen diverges CONVERGENCE OR DIVERGEN CE COMMENTS! THINGS TU WATCH -' - : fl MIGHT converge; need anmheiritefl f'l' ifcunverges 5 = —H 1" Useful with cemparisen test if the nfll term an of a series is similar to ar’H Useful fer comparison tests if the nth team an . . . . I , Ufa Senes ls sumler to Called Haneemc n Serieswhen p = 1 . —> positive -s centinueus - f {I} must he: —> decreasing - ~+ ablete integrate 2 b” is often a geometric series ere p ems. EXAI‘IIPLE 1 . 1 I - CDMM ENTSJ' - T ' * SERIES CDNVERGENCE GR DIVERGENCE _ THINGS Tn WATCH - EXAMPLE Zn“. 25,, If 11m 51 -_— C s t}, then both gems __ To find it”. consider onlg.r the terms of an that Limit Campamun a" 3,. 1:}, b” :5 fl "—3" b" have the greatest effect in the magnitude. H Converge or both diverge. C 2 fl and b mm” I file“ a coma cs Cisafinite number. - n Eat“ a s . 3 Son-lintns. - . H II. litn n = Alli: an "'1 H i! . Sent-liesng } n I "fin Must Alternatel ' a" } D 3- ‘lrnt 55:: Z ‘1" [not nltematin g If series, but 2 lgni WWWE'ES. Ehcn some tenns Z n" nonverges fitsafive} Absolute, Absolute con vorgenoe implies eon vergenoe Convergence *If diverges. might converge-need another test i ' E I ' a” . If liml—"fl-l: L DI’W then: _ :i—‘mi an Useful if It” involves factortals or nth powers. Emit! TESt DWHEES if 13’] 0f ‘3'” If a" :2- [I for ever],r n, the absolute value sign Converges if L<l ma hed‘s used huonelusive L=1 3' I raga ...
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SeriesTestsSummary - Summary of Convergence _and Divergence...

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