Calculate the following expression: the sum on $n = 1$ to infinity of: $1/(4n-3)^2 + 2/(4n-2)^2 + 1/(4n-1)^2$ using the fourier series of $f(x) = \max\{\pi- |x|, \pi/2\}.$
the first question asked to calculate the fourier series on the interval $[-\pi,\pi]$ and i got: $$f(x) \sim \frac 5 8\pi + \sum_{n = 1}^\infty \left[\cos(nx) \cdot \frac 1 \pi \cdot \left[ \frac 2 {n^2} - \frac 2 {n^2} \cos\left(\pi \frac n 2\right)\right] \right]$$
the second question asked to calculate the fourier series on the interval $[0,\pi]$ and i got: $$f(x) \sim \frac 5 8 \pi + \sum_{n = 1}^\infty \left[ \cos(2nx) \cdot \frac{(1-(-1)^n}{2\pi n^2} + \frac 1 {2n} \sin(2nx) \right]$$
hopefully got the fourier series right and u could help :)