1. The problem statement, all variables and given/known data Suppose that ∑a_n and ∑b_n are series with positive terms and ∑b_n is divergent. Prove that if: lim a_n/b_n = infinity n--->infinity then ∑a_n is also divergent. 2. Relevant equations 3. The attempt at a solution Well in attempting to write a viable solution, I have deducted that since both series have positive terms, both sequences are increasing. If ∑b_n is is divergent and the limit as n approaches infinity of a_n/b_n is infinity than ∑a_n also must be divergent. Is there anymore to this however? I think I am missing something important in the explanation but I am not too sure of what it is. Thank you!