Answer
converges to $1$
Work Step by Step
As we know that when $x \gt 0$ so, $\lim\limits_{n \to \infty} (1+\dfrac{x}{n})^{n}=e^x$
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \ln (1+\dfrac{1}{n})^{n}$
This implies that $\lim\limits_{n \to \infty} a_n=\ln (1+\dfrac{1}{n})^{n}=\ln e=1$
Thus, $\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} converges to $1$.
