(a) Assume that f(x) is function defined by J - ² 4 f(x) = for 0≤x≤. (i)Expand the function f(x) in a Fourier series. = if - < x < 0,

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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(a) Assume that f(x) is function defined by
π
if - < x < 0,
ㅠ
4
f(x) =
for 0≤x≤T.
(i)Expand the function f(x) in a Fourier
series.
(ii) Assuming that the series in part (i)
converges to f, show that
ㅠ
1 1
=
1+
-
-
3
5 7
(b)Prove the inequality
2
3² + 1 ² + ... + x² > (³ + x₂ + ... + ³ ) ²
x1
Xn
n
n
n
Transcribed Image Text:(a) Assume that f(x) is function defined by π if - < x < 0, ㅠ 4 f(x) = for 0≤x≤T. (i)Expand the function f(x) in a Fourier series. (ii) Assuming that the series in part (i) converges to f, show that ㅠ 1 1 = 1+ - - 3 5 7 (b)Prove the inequality 2 3² + 1 ² + ... + x² > (³ + x₂ + ... + ³ ) ² x1 Xn n n n
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