I am suppose to find the sum of a fourier series when $x=2$. The fourier series:
$\frac{3}{2}+\sum_{n=1}^{\infty}\left(\frac{2-2\cdot\left(-1\right)^n}{\left(n\pi\right)^2}\cdot c o s\frac{n\pi x}{2}+\frac{2\cdot\left(-1\right)^n}{n\pi}\cdot s i n{\frac{n\pi x}{2}}\right)$
The sum is supposed to be $2$, but I don't know how to derive that. Does anyone have have an idea?
My attempt at solving the problem
$x=2$
$\frac{3}{2}+\sum_{n=1}^{\infty}\left(\frac{2-2\cdot\left(-1\right)^n}{\left(n\pi\right)^2}\cdot c o s\frac{n\pi\cdot2}{2}+\frac{2\cdot\left(-1\right)^n}{n\pi}\cdot s i n{\frac{n\pi\cdot2}{2}}\right)$
$\frac{3}{2}+\sum_{n=1}^{\infty}\left(\frac{2-2\cdot\left(-1\right)^n}{\left(n\pi\right)^2}\cdot\left(-1\right)^n+\frac{2\cdot\left(-1\right)^n}{n\pi}\cdot s i n{(n\pi)}\right)$
$\frac{3}{2}+\sum_{n=1}^{\infty}\left(\frac{2\left(-1\right)^n-2}{\left(n\pi\right)^2}\right)$