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\( \displaystyle \sum_{k=1}^n k^{2015} = a \cdot n^{2016} + b\cdot n^{2015} + \ldots \).