Answer
Divergent
Work Step by Step
Suppose $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (1+\dfrac{1}{n})^n$
As we know that for all the values of $x$ we have $\lim\limits_{n \to \infty} (1+\dfrac{x}{n})^n=e^x$.
Then, $\lim\limits_{n \to \infty} (1+\dfrac{1}{n})^n=e^{1}=e \ne 0$
Thus, the series is divergent.