32 questions linked to/from About $\lim \left(1+\frac {x}{n}\right)^n$
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### Limit of $(1+ x/n)^n$ when $n$ tends to infinity [duplicate]

Does anyone know the exact proof of this limit result? $$\lim_{n\to\infty} \left(1+\frac{x}{n}\right)^n = e^x$$
### Showing that $\lim_{n \rightarrow \infty} \left( 1 + \frac{r}{n} \right)^{n} = e^{r}$. [duplicate]
I know that $\displaystyle \lim_{n \rightarrow \infty} \left( 1 + \frac{1}{n} \right)^{n} = e$, but how do I show that $$\lim_{n \rightarrow \infty} \left( 1 + \frac{r}{n} \right)^{n} = e^{r}?$$ ...