I know sum[k=1,n] k = [n(n+1)]/2, but what about Σ cos(k) =?

kapax

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May 5, 2018
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Hi, all!

Recently I calculated some summations, such as:

. . . . .\(\displaystyle \displaystyle \sum_{k=1}^n\, k\, =\, \dfrac{n\,(n\, +\, 1)}{2}\)

The idea of the summation of cos(k) just popped up in my head:

. . . . .\(\displaystyle \displaystyle \sum_{k=1}^n\, \cos(k)\, =\, ?\)

I have googled a lot, but none of the results seems to be about this kind of question.
 

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