More fun in 2015, Part 6

Algebra Level 5

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

For constants $a,b$ , we have $\displaystyle \sum_{k=1}^n k^{2015} = a \cdot n^{2016} + b\cdot n^{2015} + \ldots$ .

Find $\frac{b}{a}$ .