Polynomial Sum Power of root

Algebra Level 5

\[ \large x^{2015} + 2x^{2014} + 3x^{2013} + \ldots + 2015x + 2016 = 0 \]

Let \(x_1, x_2, \ldots , x_{2015} \) be the roots of the equation above. Find the value of the summation below.

\[ \large \sum_{n=0}^{2014} \sum_{k=1}^{2015} (x_k)^n \]

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