## Thomas' Calculus 13th Edition

The nth partial sums are: $s_n=(\ln (1) - \ln (2))+(\ln (2) - \ln (3))+.......+(\ln (n) - \ln (n+1))=-\ln (n+1)$ Now apply limis. Then $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} -\ln (n+1)=-\infty$ This shows that the sequence of partial sums $s_n$ diverges. Hence, the series also diverges.