I am trying to figure out a limit, but am getting a bit stuck.

$\displaystyle

\lim_{n\to \infty} \left(1 + a\frac{t}{n} + a^2\frac{t^2}{2n^2} + a^3\frac{t^3}{3!n^3} + a^4\frac{t^4}{4!n^4}\right)^n

$

Obviously,

$\displaystyle

\lim_{n\to \infty} \left(1 + a\frac{t}{n}\right)^n = e^{at}

$

but I am having trouble extending this.