I have to find the Fourier series expansion of the function $f(x)$=$x^2$ for $-\pi <x< \pi$ and using it I have to show that,
i) $1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}...$ = $\frac{\pi^2}{6}$
ii) $1-\frac{1}{4}+\frac{1}{9}-\frac{1}{16}+-...$ = $\frac{\pi^2}{12}$
I found out the Fourier expansion, it turned out to be,
$\frac{\pi^2}{6}$ - $2\left(\cos x-\frac{1}{4}\cos2x+\frac{1}{9}\cos3x-\frac{1}{16}\cos4x…\right)$
How do I proceed further, any ideas?
