Series-1 - 'NAME Divergence Test { l l .42.) Integral Test...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 'NAME Divergence Test { l l .42.) Integral Test (11.4.5) Comparison Test (11.5.1) Ratio m (11.5.2) Root Tat (11.5.3) Limit Comparison Test (11.6.3) Alternating Series Test (11.7.!) Ratio Test for Absolute Convergence | (H.725) Review of Convergence Tats If lirn as = 0, Eek may or may no _-'.a If lim in, 5* 0. th k—+a en Eng diverges. converge. Let 23;; be a series with positive terms. and let fix) be the function that results when it is replaced by x in the formula for Hg. Iff is decreasing and continuous forx 2 1, then 2 in: and fflflx) d): 1 both converge or both diverge. Use this test when fix) is easy to integrate. This test only applies to series that have positive terms. Let Eat and 25;: he series with nonnegative terms such that aisbi. az'sbz.....aistri.... Hiring converges. then Eng converges, and ifZak diverges, then 2.5;; diverges. Use this test as a last resort; other tests are often easier to apply. This test only applies to series with nonnegative tel-Iris. Let Em. be a series with positive terms and suppose Hint __ _ P lim Try this test when it}: involves k—+2 in: . I factorials or kth powers. (3} Series converges ifp < l. (13) Series diverges ifp >_l orp = +31. (c) No conclusion it'p = I. Let Em. be a series with positive terms such that p = lim 5m; k-«i-a Try this test when in. involves kth powers. (a) Series converges ifp < 1. (in) Series diverges ifp > 1 or p =-+=n. (c) No conclusion ifp = l. Let 2a,. and 213,. be series with positive terms such that _ : This is easier to apply than the - comparison test, but still requires some skill in choosing the series I Ebk for comparison. _ 1- E p _ kill-la bk IfO < p < +66, then both series converge or both diverge. The series alflflg+33—a4+"‘ This test applies only to I-n+a--a+a—--- . . 1 2 3 4 I alternating series. anti-i: ) a b y 5 it is assumed that {I}; > 0 for all k- 1 2 3 [bi Iim ah = 0 K k—vba Let Erikle a series with nonzero terms such that p = lim' ift’kni k-ai-x [Hki The series need not have positive terms and need not be alternating to use this test. '1 (a) Series converges absolutely ifp < I. ‘ (13) Series diverges ifp > 1 mp = +96. I (c} No conciusion ifp = I. i erEflIKPEI manage .9 5222:23m nozcnnmnznn . . Z: . . :2. Es: F5 .m E: a: H o. .Iliv mEEm aEmnmnm 4.3.. E. 251?. 09.55:? meanm 832m? 2 E A p. waanm "E: mmlnm Ecnnmnm :. N H. a+aw+awm+...w Doom MEL nonfimgmnuV T36? 98 3. 5m 833:3: Fara: manna:— ..:u.m_. 3:0 22:. ca 2.: So. .9: E 53.: Zouflammmzcn 822m Ea}: 352:5 no=<a~mh=nn 01min: manna noncnammm. 2c om Earn FM? H. 3T 3 + 3 I . .. 7.: mznnzuzum union“ 37:333....“ .813 “J man «1:: we: nm: as 2:: 25.15::— 95? .9. 8.5:: :53 "3.5:.an coorm. mnlmm nc=<nnmnm =. P. Iv a manna qmcnamnm mm P. J? a. ...
View Full Document

Page1 / 2

Series-1 - 'NAME Divergence Test { l l .42.) Integral Test...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online