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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 $\frac{b}{a}$.

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