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3. (a) Show that the Fourier series for f(x) = x², –T < x < n, is n-1 Cos(nx) 4(-1)"-1 n2 n=1 (b) Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. (c) Show that E = 5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de- veloped) n=1 n² (d) Show that E n+1 n=1 n2

3. (a) Show that the Fourier series for f(x) = x², –T < x < n, is n-1 Cos(nx) 4(-1)"-1 n2 n=1 (b) Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. (c) Show that E = 5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de- veloped) n=1 n² (d) Show that E n+1 n=1 n2

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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3. (a) Show that the Fourier series for f(x) = x², –n < x < T, is 42(-1)n-1 Cos(nx) n2 n=1 (b) Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. (c) Show that E = 5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de veloped) 1 (d) Show that En=1 (-1)n+1 n2 12
Transcribed Image Text:3. (a) Show that the Fourier series for f(x) = x², –n < x < T, is 42(-1)n-1 Cos(nx) n2 n=1 (b) Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. (c) Show that E = 5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de veloped) 1 (d) Show that En=1 (-1)n+1 n2 12
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