I was going through the following proof of the fact that $\sum_{n = 0}^\infty x^n/n! = \lim_{n\to\infty}(1 + x/n)^n$ at ProofWiki:
The Power over Factorial entry states that $x^n/n!\to 0$ for any real $x$.
However, I am at loss on how this helps in concluding that $$ 1 + x + \left( \frac{n - 1}{n} \right)\frac{x^2}{2!} + \cdots $$ goes to the claimed limit $1 + x + x^2/2! + \cdots$.
Any help?