PLEASE EXPLAIN If bn is a divergent series is an unknown ser

PLEASE EXPLAIN!

If bn is a divergent series, is an unknown series, and then diverges. Evaluate the following as true or false. The series converges.

Solution

We know 1/n is a divergent series. lim (1/ln n / 1/n)= n/ln n By L\'Hospital\'s rule lim n/ln n as n gets large is infinity because we have 1/1/n= n. So False. 1/ln n does not converge.