6. Let a be a real number. Consider the series where a, = cos(na); 2n +1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally.
6. Let a be a real number. Consider the series where a, = cos(na); 2n +1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally.
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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Transcribed Image Text:6. Let a be a real number. Consider the series
where an =
cos(na):
2n +1
n=0
(a) Is it possible to find an a > 0 such that the above series is both absolutely convergent
and conditionally convergent? Briefly explain your reasoning.
(b) Find all a > 0 such that the series diverges.
(c) Find all a > 0 such that the series converges absolutely.
(d) Find all a > 0 such that the series converges conditionally.
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