Prove that for all $x\in \mathbb{Z}$ the sequence $(1+\frac{x}{n})^n$ is converging and it's limit is $e^x$.
I'm not even sure how to start this one. How can I even open $(1+\frac{x}{n})$ to something I can work with? I do know $\lim(1+\frac{1}{n})^n=e$, but not sure how to get from one to the other...