Answer
Diverges
Work Step by Step
The kth term formula of the series is given by: $a_k=(1+\dfrac{2}{k})^{k}$
Thus, $\lim\limits_{k \to \infty}a_k=\lim\limits_{k \to \infty}(1+\dfrac{2}{k})^{k} \\=e^2$
Therefore, we can see that the limit of kth term is not zero, this implies that the series diverges.
