More fun in 2015, Part 6

Algebra Level 5

We are told that k=0nkm \displaystyle \sum_{k=0}^n k^m is a polynomial in nn of degree m+1m+1.

For constants a,ba,b, we havek=1nk2015=an2016+bn2015+ \displaystyle \sum_{k=1}^n k^{2015} = a \cdot n^{2016} + b\cdot n^{2015} + \ldots .

Find ba\frac{b}{a}.

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