Parseval's Identity

Homework Statement

Obtain the result of the infinite sum $$1+\frac{1}{9}+\frac{1}{25}+\cdot\cdot\cdot$$

By applying Parseval's Identity to the fourier series expansion of
0 if $$-\frac{\pi}{2} < x < \frac{\pi}{2}$$
1 if $$\frac{\pi}{2} < x < \frac{3\pi}{2}$$

Homework Equations

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

The Attempt at a Solution

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

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