Answer
converges to $0$
Work Step by Step
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} [\ln n - \ln (n+1)]$
This implies that $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} [\ln n - \ln (n+1)]$
and $a_n=\lim\limits_{n \to \infty} \ln (\dfrac{n}{n+1}) =\ln \lim\limits_{n \to \infty} \dfrac{n}{(n+1)}=\ln (1)=0$
Thus, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} converges to $0$.
