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∑k=02014(22+e2kπi/2015)\sum_{k=0}^{2014}\left(\frac{2}{2+e^{2k\pi i/2015}}\right)k=0∑2014(2+e2kπi/20152)
Let SSS denote the value of the summation above. Which of the answer choices must be true?
Bonus question: Can you generalize this? If Sn=∑k=0n−1(22+e2kπi/n)\displaystyle S_n=\sum_{k=0}^{n-1}\left(\frac{2}{2+e^{2k\pi i/n}}\right)Sn=k=0∑n−1(2+e2kπi/n2), what is the relationship between SnS_nSn and nnn?
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