Answer
Converges to $e^{2}$
Work Step by Step
Given: $a_n=(1+\frac{2}{n})^{n}$
We know that $\lim\limits_{n \to \infty}(1+\frac{x}{n})^{n}=e^{x}$
Thus,
$a_n=\lim\limits_{n \to \infty}(1+\frac{2}{n})^{n}=e^{2}$
Therefore, the sequence converges to $e^{2}$.
