Past, Present, or Future?

Algebra Level 3

\[\sum_{k=0}^{2014}\left(\frac{2}{2+e^{2k\pi i/2015}}\right)\]

Let \(S\) denote the value of the summation above. Which of the answer choices must be true?

Bonus question: Can you generalize this? If \(\displaystyle S_n=\sum_{k=0}^{n-1}\left(\frac{2}{2+e^{2k\pi i/n}}\right)\), what is the relationship between \(S_n\) and \(n\)?

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