## University Calculus: Early Transcendentals (3rd Edition)

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.