Find the value of the sum

Geometry Level pending

If the following sums to some rational, a b -\frac{a}{b} , for some coprime integers a , b a,b , find a + b a+b . k = 1 n cos 2 k π 2 n + 1 . \displaystyle\sum_{k=1}^{n} \cos \frac{2k\pi}{2n + 1}.


The answer is 3.

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