Write TRUE if the statement is always correct and FALSE if otherwise. (a) If an >0 for all n E N, then > an does not converge conditionally. n=1 (b) If the power series > a,(x + 1)" converges at r = 2, then ) (-1)"a, converges. n=1 n=1 (c) If an < bn for all n e N and ) an is divergent, then b, is divergent. n=1 n=1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Write TRUE if the statement is always correct and FALSE if otherwise.
(a) If an >0 for all n E N, then > an does not converge conditionally.
n=1
(b) If the power series > a,(x + 1)" converges at r = 2, then ) (-1)"a, converges.
n=1
n=1
(c) If an < bn for all n e N and ) an is divergent, then b, is divergent.
n=1
n=1
Transcribed Image Text:Write TRUE if the statement is always correct and FALSE if otherwise. (a) If an >0 for all n E N, then > an does not converge conditionally. n=1 (b) If the power series > a,(x + 1)" converges at r = 2, then ) (-1)"a, converges. n=1 n=1 (c) If an < bn for all n e N and ) an is divergent, then b, is divergent. n=1 n=1
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