Let $l\in\mathbb{Z}$ and $N\in\mathbb{N}$. I need to prove the following: \begin{equation} \sum_{j=0}^{N-1}\cos\left(l\frac{\left(2j+1\right)\pi}{2N} \right)=0 \end{equation} I tried to use Euler formula and then sum the first $N$ terms of the geometric serie I get, but it didn't work. Any ideas?
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1Compare the $j$ term with the $N-1-j$ term. – Angina Seng Apr 15 '19 at 16:38
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Thanks! @LordSharktheUnknown – avati91 Apr 15 '19 at 16:49