Past, Present, or Future?

Algebra Level 3

k=02014(22+e2kπi/2015)\sum_{k=0}^{2014}\left(\frac{2}{2+e^{2k\pi i/2015}}\right)

Let SS denote the value of the summation above. Which of the answer choices must be true?

Bonus question: Can you generalize this? If Sn=k=0n1(22+e2kπi/n)\displaystyle S_n=\sum_{k=0}^{n-1}\left(\frac{2}{2+e^{2k\pi i/n}}\right), what is the relationship between SnS_n and nn?

×

Problem Loading...

Note Loading...

Set Loading...