Consider the square wave function

\[f(x)=\left\{\begin{array}{rc} 1, & 0

a. Find the Fourier series representation of this function and plot the first 50 terms.

b. Apply Parseval's identity in Problem 8 to the result in part a.

c. Use the result of part \(\mathrm{b}\) to show \(\frac{\pi^{2}}{8}=\sum_{n=1}^{\infty} \frac{1}{(2 n-1)^{2}}\).