4. (a) Test the series n=1 for convergence and divergence. (-1)^ (1+x)" 2n n² Hence, deduce that + 32 52 f(x) = (b) Find the Fourier sine series of the function x₂ 0
4. (a) Test the series n=1 for convergence and divergence. (-1)^ (1+x)" 2n n² Hence, deduce that + 32 52 f(x) = (b) Find the Fourier sine series of the function x₂ 0
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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Question
![4. (a) Test the series
(-1)^(1+x)"
2n n²
n=1
for convergence and divergence.
Hence, deduce that
(b) Find the Fourier sine series of the
function
* Ο
f(x) =
MIN
HIN
πt 2
8
2
<x≤R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce595974-4dd6-4a2d-82b8-66623a5a1974%2Ff85a4699-747a-4959-aa82-1799a22b0055%2F8mlrnpe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. (a) Test the series
(-1)^(1+x)"
2n n²
n=1
for convergence and divergence.
Hence, deduce that
(b) Find the Fourier sine series of the
function
* Ο
f(x) =
MIN
HIN
πt 2
8
2
<x≤R
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