Prove that $\sum_{i=1}^k i!$ can never be of the form $n^m$ (where $n,m\in\mathbb N$ and $m\ge 2$) for $k\ge 4$.
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers