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TheFerruccio

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## Homework Statement

Obtain the result of the infinite sum [tex]1+\frac{1}{9}+\frac{1}{25}+\cdot\cdot\cdot[/tex]

By applying Parseval's Identity to the fourier series expansion of

0 if [tex]-\frac{\pi}{2} < x < \frac{\pi}{2}[/tex]

1 if [tex]\frac{\pi}{2} < x < \frac{3\pi}{2}[/tex]

## Homework Equations

[tex]2a_0^2+\sum_n{(a_n^2+b_n^2)}\leq\frac{1}{\pi}\int_{-\pi}^{\pi}\! f^2(x) \, \mathrm{d}x.[/tex]

## The Attempt at a Solution

I got the solution to the fourier series, and I know it's correct.

The terms for [tex]a_n[/tex] in the fourier series expansion are [tex]\frac{-2}{n\pi}[/tex] if n=1,5,9,13,..., and [tex]\frac{2}{n\pi}[/tex] if n=3,7,11,15,...

The [tex]b_n[/tex] terms are 0, since it is an even function about 0.

I'm just not sure how to use this information in Parseval's Identity.

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