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2. Find the Fourier series expansion of: fo, f(x) = -1 < ¢ < 0 sin Tr, 0< x <1 and then use it to find the values of the following infinite sums: 1. (a) 3 ... 15 35 63 4n? 1. 1 1 (-1)"+1 (b) 3 +. 35 15 ... 63 4n2 1 (c) ... 143 255 16n2 1 1 1 (d) 3 --.. 152 352 632 (4n2 – 1)2

2. Find the Fourier series expansion of: fo, f(x) = -1 < ¢ < 0 sin Tr, 0< x <1 and then use it to find the values of the following infinite sums: 1. (a) 3 ... 15 35 63 4n? 1. 1 1 (-1)"+1 (b) 3 +. 35 15 ... 63 4n2 1 (c) ... 143 255 16n2 1 1 1 (d) 3 --.. 152 352 632 (4n2 – 1)2

Advanced Engineering Mathematics
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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2. Find the Fourier series expansion of: So. sin TI, 0<r<1 -1< 1 < 0 f(x) = and then use it to find the values of the following infinite sums: 1. 1. 1 (a) +. +. 63 +. 3 15 35 4n? 1. (-1)n+1 (b) 3 1 +. 35 15 63 4n2 1 1 15 63 143 255 16n2 1 1 1 (d) 3 352 (4n2 - 1)2 152 632
Transcribed Image Text:2. Find the Fourier series expansion of: So. sin TI, 0<r<1 -1< 1 < 0 f(x) = and then use it to find the values of the following infinite sums: 1. 1. 1 (a) +. +. 63 +. 3 15 35 4n? 1. (-1)n+1 (b) 3 1 +. 35 15 63 4n2 1 1 15 63 143 255 16n2 1 1 1 (d) 3 352 (4n2 - 1)2 152 632
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