Answer
Converges to $1$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \ln (1+\dfrac{1}{n})^{n}$
Since, $\lim\limits_{n \to \infty} (1+\dfrac{x}{n})^{n}=e^x$ when $x \gt 0$
So, $\lim\limits_{n \to \infty} a_n=\ln (1+\dfrac{1}{n})^{n}=\ln e=1$
Hence, $\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} is convergent and converges to $1$
