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(a) If the nth term of a sequence approaches 1 as n→ 0, then its sequence of partial sums converges to some value. (b) The sequence a, 4n2 - is bounded. (c) ; is a lower bound for the sequence a, 4n2 - 1

(a) If the nth term of a sequence approaches 1 as n→ 0, then its sequence of partial sums converges to some value. (b) The sequence a, 4n2 - is bounded. (c) ; is a lower bound for the sequence a, 4n2 - 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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True or False. If false provide an explanation or a counterexample.
(a) If the nth term of a sequence approaches 1 as n → x, then its sequence of partial sums converges to some value. 1 (b) The sequence an is bounded. 4n2 – 1 (c) 1 is a lower bound for the sequence a, = 4n2 - 1 (d) E(-1)*+1, /2n -1 is absolutely convergent. n=1 (e) > n! z" converges for all r. n=1
Transcribed Image Text:(a) If the nth term of a sequence approaches 1 as n → x, then its sequence of partial sums converges to some value. 1 (b) The sequence an is bounded. 4n2 – 1 (c) 1 is a lower bound for the sequence a, = 4n2 - 1 (d) E(-1)*+1, /2n -1 is absolutely convergent. n=1 (e) > n! z" converges for all r. n=1
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