$d_n=(1+(2/n))^n$ converge or diverge and find the limit? I know the answer is $e^2$ and I'd like to use L'Hopital's rule because this is an indeterminate form. Can someone explain how to get there?
$$d_n=\left(1+\frac{2}{n}\right)^n$$

Using the well known limit
$$\lim_{n\to\infty}\left(1+\frac1n\right)^n=e$$
we can get
$$\begin{align}
\lim_{n\to\infty}\left(1+\frac2n\right)^n & =\lim_{n\to\infty}\left(1+\frac1{n/2}\right)^n\\
& = \lim_{m\to\infty}\left(1+\frac1m\right)^{2m}\quad m=n/2\\
& = \lim_{m\to\infty}\left[\left(1+\frac1m\right)^m\right]^2\\
& = e^2
\end{align}$$
