Answer
$e^{12}$
Work Step by Step
We are given the sequence:
$\left\{\left(1+\dfrac{4}{n}\right)^{3n}\right\}$
Rewrite the general term of the sequence:
$\left(1+\dfrac{4}{n}\right)^{3n}=\left(\left(1+\dfrac{1}{\frac{n}{4}}\right)^{n/4}\right)^{12}$
Use the fact that $\lim\limits_{n \to \infty} \left(1+\dfrac{1}{n}\right)^n=e$ to determine the limit of the given sequence:
$\lim\limits_{n \to \infty} \left(\left(1+\dfrac{1}{\frac{n}{4}}\right)^{n/4}\right)^{12}=\left(\lim\limits_{n \to \infty} \left(1+\dfrac{1}{\frac{n}{4}}\right)^{n/4}\right)^{12}=e^{12}$
