I need help with that sum $$\sum_{k=1}^N \csc^2\left(\frac{k\pi}{2N}\right)$$ - it is given in many tables as a standard result, but I can't figure it out. I know how to do $\sin^2$ and $\cos^2$, but the method I am using (multiplying by some half angle function like $\sin\left(\frac{\pi}{4N}\right)$) doesn't seem to work. I also tried splitting in $1+\cot^2$ but the half angle formula for $\cot$ is not nice.
Any hints will be appreciated.
$\endgroup$ 5 Reset to default
