Would someone be able to help me solve this?
The function $f:(0,\pi]\to\mathbb{R}$ is defined by $$f(x) = \begin{cases} x & 0 < x \le \frac\pi2 \\[5pt] 0 & \frac\pi2 < x \le \pi \end{cases}$$ Find the coefficients and evaluate the series $\sum_{n=1}^\infty \frac{1}{(2n-1)^2}$.
Thank you. I solved to find $ b_n=\frac{-1}{n^2\pi}\sin(\frac{n\pi}{2})$.
But I'm not sure if it's correct since I can't seem to use to get the final answer, thank you.