Answer
Converges
Work Step by Step
Apply the root test.
Therefore, $ L=\lim\limits_{k \to \infty} |a_k|^{1/k}=\lim\limits_{k \to \infty} (\dfrac{n}{n+1})^n \\=\lim\limits_{k \to \infty} \dfrac{1}{(\dfrac{n+1}{n})^n}\\=\lim\limits_{k \to \infty} \dfrac{1}{(1+\dfrac{1}{n})^n}\\=\dfrac{1}{e} \lt 1$
So, we can conclude that the given series converges by the root test.