Series-1

# Series-1 - 'NAME Divergence Test l l.42 Integral...

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

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

View Full Document
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

## This note was uploaded on 04/18/2008 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

### Page1 / 2

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

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

View Full Document
Ask a homework question - tutors are online