2. Determine the Fourier series expansion of the periodic function f(x) f(x+2) = f(x), x E R. Use this series to prove the following: 1 1 (a) 1+ + 22 1 (b) 1 + 22 1 32 + 1 1 4² 12 4 for x = [-T, π), E

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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2. Determine the Fourier series expansion of the periodic function f(x)
f(x), x E R. Use this series to prove the following:
f(x + 2π)
1
(a) 1+
(b)
1
2²
2²
3²
1
4²
4²
+
||
π²
6
πT²
12
4
for x = [-π, π),
Transcribed Image Text:2. Determine the Fourier series expansion of the periodic function f(x) f(x), x E R. Use this series to prove the following: f(x + 2π) 1 (a) 1+ (b) 1 2² 2² 3² 1 4² 4² + || π² 6 πT² 12 4 for x = [-π, π),
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