(4) Q4 MULTIPLE CHOICE One answer only. If a series an is convergent and (bn)neN is a bounded sequence, then anbn is convergent. a. False, here is a counter-example: an = = (-1)"/√n and bn = (-1)". b. True, here is an example: an =1/√√n, bn = (-1)". c. True, because anbn ≤ Man (with M a bound of (bn)neN) so by comparison test, anbn converges. d. False, because even if they are bounded the values bn could be large and prevent anbn from being small enough so that anbn converges.
(4) Q4 MULTIPLE CHOICE One answer only. If a series an is convergent and (bn)neN is a bounded sequence, then anbn is convergent. a. False, here is a counter-example: an = = (-1)"/√n and bn = (-1)". b. True, here is an example: an =1/√√n, bn = (-1)". c. True, because anbn ≤ Man (with M a bound of (bn)neN) so by comparison test, anbn converges. d. False, because even if they are bounded the values bn could be large and prevent anbn from being small enough so that anbn converges.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(4) Q4
MULTIPLE CHOICE
One answer only
If a series an is convergent and (bn)neN is a bounded sequence, then anbn is convergent.
a. False, here is a counter-example: an
b. True, here is an example: an = 1/√√n, bn = (-1)".
c. True, because anbn ≤ Man (with M a bound of (bn)neN) so by comparison test, Σanbn converges.
d. False, because even if they are bounded the values bn could be large and prevent anbn from being small
enough so that Σanbn converges.
=
(−1)n/√n and bn = (−1)².
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