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**scounged** I'm given the function $\displaystyle f(x)=\sum_{n=0}^{\infty}\frac{x^n}{n!}$ and I'm supposed to prove that $\displaystyle f(x)=e^x$.

I was thinking that I should use a different representation of e, namely:

$\displaystyle e^x=\lim_{n \rightarrow \infty} (1+\frac{x}{n})^n$

and use the binomial theorem to expand it as an infinite series, but I can't get it to work properly. If it's possible, then how should it be done?

Otherwise, any hints on how I should prove it instead?