Pascal's identity

#stub

\begin{aligned} (n + 1)^{k + 1} - 1 & = \sum_{m = 1}^{n} ((m + 1)^{k + 1} - m^{k + 1} \\ = \sum_{p = 0}^{k} (\binom{k + 1}{p}) (1^{p} + 2^{p} + \dots + n^{p}) \end{aligned}