## Calculus (3rd Edition)

$e^4$
Let $x=\frac{n}{4}$, then we have $$\lim _{n \rightarrow \infty}\left(1+\frac{4}{n}\right)^{n}=\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{4x}\\ =\left(\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{x}\right)^4=e^4,$$ where we used the formula $\lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^{n}=e$.