- #1

richyw

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## Homework Statement

a) Show that the Fourier Cosine Series of [itex]f(x)=x,\quad 0\leq x<L[/itex] is

[tex]x ~ \frac{L}{2}-\frac{4 L}{\pi ^2}\left[\left(\frac{\pi x}{L}\right)+ \frac{\cos\left(\frac{3\pi x}{L}\right)}{3^2}+\frac{\cos\left(\frac{5 \pi x}{L}\right)}{5^2}+\dots\right][/tex]

b) use the above series to evaluate the sum[tex]1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...[/tex]

## Homework Equations

Fourier Cosine Series General form

## The Attempt at a Solution

So I have done part a, but I am lost on how to do part b. I don't understand how to get the even terms? Perhaps I need to differentiate the series, which would pull an n out, making the n's even.

To differentiate term by term a cosine series I need f'(x) to be piecewise continuous. Which I think it is.

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