Let $a_{0}, a_{1}, a_{2}, \ldots$ be integers such that there exists an $M$ with $M \geqslant\left|a_{n}\right|$ for all $n$. Show that, if infinitely many of the $a_{n}$ are non-zero, then $\sum_{n=0}^{\infty} \frac{a_{n}}{n !}$ is an irrational number.