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I found the Fourier Series for Cosh(x) in the range -1 to +1 and discovered that:

[tex]f(x)=sinh(1)(1+\sum_{n=1}^\infty\frac{(-1)^n}{1+n^2\pi^2}cos(n\pi x)[/tex])

Now, I have to integrate the series twice to prove that:

[tex]\sum_{n=1}^\infty\frac{(-1)^n}{n^2\pi^2(1+n^2\pi^2)}cos(n\pi x)=\frac{1}{2}(\frac{1}{sinh(1)}-\frac{5}{6})[/tex]

I've been looking at this for ages! I can obtain the Left hand side pretty easy, but nothing like the Right. I'm really stuck here and I've really been trying. If anyone can help I'd be really grateful.

Thank-you in advance.

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# Fourier Series for Cosh

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