Answer
$ e^6$
Work Step by Step
Let $ x=\frac{n}{3}$, then we have
$$\lim _{n \rightarrow \infty}\left(1+\frac{3}{n}\right)^{2n}=\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{6x}\\
=\left(\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{x}\right)^6=e^6,$$
where we used the formula $\lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^{n}=e $.
