A Sum of High Cosine Powers

★ 7/10combinatoricscomplex numberstrigonometryRoots of Unity FilterBinomial Theorem

Problem

Compute

∑k=11008cos⁡2016kπ1008.\sum_{k=1}^{1008} \cos^{2016}\frac{k\pi}{1008}.

Answer

Solution

Difficulty7/10
Topicscombinatorics, complex numbers, trigonometry, Roots of Unity Filter, Binomial Theorem

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