1. The problem statement, all variables and given/known data Find the limit of this sequence: (-1)n(2n3)/(n3+1) 2. Relevant equations 3. The attempt at a solution At first glance I would attempt to use the absolute value theorem which gives an answer of 2 as n approaches infinite. My question is, when the theorem fails ( limit =/ 0) then does that mean the sequence is divergent? I haven't seen any documentation that explicitly states an is divergent if the absolute value theorem doesn't hold.