Currently I'm working with Fourier series, and I'm trying to understand a proof, it starts like this:

$2\pi D_n(u) = \sum_{n=-N}^Ne^{inu} = e^{-iNu}\sum_{n=0}^{2N}e^{inu} = e^{-inu}\frac{1-e^{i(2N+1)u}}{1-e^{iu}}$

I cannot understand this equality, can someone help me out on this one, any help is appreciated at this point.


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