SOLVED:(a) Use Parseval's identity and the Fourier series expansion (x)/(2)=∑n=1^∞ ((-1)^n+1)/(n) sinn x, -π<x<πto obtain ∑n=1^∞ (1)/(n^2)=(π^2)/(6) (b) From (a) obtain that ∑k=1^∞ (1)/((2 k)^2)=(π^2)/(24). (c) Combine (a) and (b) to derive the identity ∑k=0^∞ (1)/((2 k+1)^2)=(π^2)/(8)
SOLVED:(a) Use Parseval's identity and the Fourier series expansion (…
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