Determine whether $a_n = (1+\frac{2}{n})^{n}$ converges or diverges. If it converges, find the limit.
So I tried to say that $a_n = (1+\frac{2}{n})^{n} \Rightarrow \ln(a_n) = n\ln(1+\frac{2}{n})$. Unfortunately I don't know what the next step is since I think that $n \rightarrow \infty$ as $n \rightarrow \infty$ and that $\ln(1+\frac{2}{n}) \rightarrow 0$ as $n\rightarrow \infty$, but somehow the solution is $e^{2}$... Can someone please help fill me in on the steps in-between? Thanks!