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Math Help - Fourier series to calculate an infinite series

  1. #1
    MHF Contributor arbolis's Avatar
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    Fourier series to calculate an infinite series

    I'm not asking the solution, but rather the main idea of how to solve the part 2:
    1)Find the Fourier development of f(t)=|t| with -\pi \leq t \leq \pi.
    2)Show using the previous result that \sum _{k=0}^{\infty} \frac{1}{(2k+1)^2}=\frac{\pi ^2}{8}.
    Attempt: Is it just by using Parseval's theorem?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by arbolis View Post
    I'm not asking the solution, but rather the main idea of how to solve the part 2:
    1)Find the Fourier development of f(t)=|t| with -\pi \leq t \leq \pi.
    2)Show using the previous result that \sum _{k=0}^{\infty} \frac{1}{(2k+1)^2}=\frac{\pi ^2}{8}.
    Attempt: Is it just by using Parseval's theorem?
    I do believe you could use Parseval's theorem for part 2.
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