Answer
Converges to $0$
Work Step by Step
Given:$a_n=[ln(n+1)-ln(n)]$
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}[ln(n+1)-ln(n)]$
$=\lim\limits_{n \to \infty}ln[\frac{n+1}{n}]$
$=\lim\limits_{n \to \infty}ln(\frac {n}{n}+\frac{1}{n})$
$=ln(1+0)$
$=ln1$
$=0$
Hence, the sequence converges to $0$.
