Find the Fourier series expansion of: 0, -1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 46E
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Find the Fourier series expansion of:
0,
f (x) =
-1< x < 0
sin Tx, 0<x <1
and then use it to find the values of the following infinite sums:
1
1
1
1
1
(a)
3
+
+
63
+...
15
35
4n2 – 1
1
(-1)"+1
1
1
(b)
3
-
-
...
15
35
63
4n2 – 1
1
1
1
(c)
15
+
16n2 – 1
+
...
...
63
143
255
1
1
1
1
+
632
1
(d)
32
+.
(4n2 – 1)2
152
352
Transcribed Image Text:Find the Fourier series expansion of: 0, f (x) = -1< x < 0 sin Tx, 0<x <1 and then use it to find the values of the following infinite sums: 1 1 1 1 1 (a) 3 + + 63 +... 15 35 4n2 – 1 1 (-1)"+1 1 1 (b) 3 - - ... 15 35 63 4n2 – 1 1 1 1 (c) 15 + 16n2 – 1 + ... ... 63 143 255 1 1 1 1 + 632 1 (d) 32 +. (4n2 – 1)2 152 352
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