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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