Answer
Converges to $0$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} [\ln n - \ln (n+1)]$
So, $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \lim\limits_{n \to \infty} [\ln n - \ln (n+1)]=\lim\limits_{n \to \infty} \ln (\dfrac{n}{n+1}) =\ln (\lim\limits_{n \to \infty} [\dfrac{n}{n+1})]=\ln 1=0$
Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is Convergent and converges to $0$
