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Is there a problem on basic complex analysis, i need to find an expression for the result of the finite sum

$ \sum \limits_{n=0}^{M-1} e^a$, where $a=(i \frac{2\pi}{M{}}nk)$, this result must depend on $k$, i have thought to use Euler identity to expand the Euler constant in the sum, but it is a good strategy?

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Hint: geometric series. –  Robert Israel Sep 7 '12 at 0:46
There is a much simpler approach. What would you do when you evaluate the sum $1+r+r^2+\cdots+r^{n-1}$? –  sos440 Sep 7 '12 at 0:49

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