I need help proving lim as n -> infinity of (1 + a/n)^n = e^a

We can build off the classic \lim_{t\to\0}(1+t)^{\frac{1}{t}}=e

We have:

\lim_{n\to\infty}(1+\frac{a}{n})^{n}

Let t=\frac{a}{n}, \;\ n=\frac{a}{t}

Now, as {n\to\infty}, then {t\to\0}

\lim_{t\to\0}(1+t)^{\frac{a}{t}}

Factor out the a:

\lim_{t\to\0}\left[(1+t)^{\frac{1}{t}}\right]^{a}

As we can now see, the inner limit is e and we have e^{a}