(a) Prove the convergence of the series given by arctann Σ(-1)"! √n (b) Determine whether the series Σ(1) -1. √√T n+4 converges absolutely, conditionally or not at all. (e) Find the radius and interval of conver- gence of the series [³"- 3" + (-2)" 71 n=1 -(x + 1)".

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Prove the convergence of the series given
by
arctan n
Σ(-1)" √n
n=1
(b) Determine whether the series
Σ(-1)-1_√n
n=1
n+4
converges absolutely, conditionally or
not at all.
(c) Find the radius and interval of conver-
gence of the series
Σ
3+(-2)",
n
-(x + 1)".
Transcribed Image Text:(a) Prove the convergence of the series given by arctan n Σ(-1)" √n n=1 (b) Determine whether the series Σ(-1)-1_√n n=1 n+4 converges absolutely, conditionally or not at all. (c) Find the radius and interval of conver- gence of the series Σ 3+(-2)", n -(x + 1)".
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