Answer
converges to $0$
Work Step by Step
Here, $\int_1^1 \dfrac{1}{n} dx$
and $[\ln x]_1^n=\ln n -\ln 1=\ln n-0=\ln n$
Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{\ln n}{n}$
But $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{\ln n}{n}=\dfrac{\infty}{\infty}$
This shows that the limit has an Indeterminate form so, we will use L-Hospital's rule.
This implies that $\lim\limits_{n \to \infty} \dfrac{1}{n}=0$
Thus, {$a_n$} is Convergent and converges to $0$.
