Answer
The sequence $a_n$ converges to $2^{1/3}$.
Work Step by Step
We have
$$\lim_{n\to \infty}a_n=\lim_{n\to \infty}
\left(2+\frac{4}{n^{2}}\right)^{1 / 3}
\\
=\left(2+0\right)^{1 / 3}=2^{1/3}.$$
Hence, by Theorem 1, the sequence $a_n$ converges to $2^{1/3}$.
