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
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
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0a14c9c-77b1-4783-af38-f4283322f597%2F8395ffb2-dc75-42f8-80dc-0196c68550d2%2F5w6rbwj_processed.png&w=3840&q=75)
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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