Answer
Diverges
Work Step by Step
Here, we have:
$ s_n=(\ln (1) - \ln (2))+(\ln (2) - \ln (3))+.......+(\ln (n) - \ln (n+1))=-\ln (n+1)$
Thus, we have the sum $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} -\ln (n+1)=-\infty$
This shows that the sequence of partial sums diverges and thus the series also diverges.
