n^2 - 1 / (n^3 + 6n) If I use the nth divergence test, I plug ∞ in (limit as n -> ∞) for n and since the degree on the bottom is larger I get 0, which means it converges. However, if I use the limit comparison test and compare it to: n^2/n^3, which = 1/n, which diverges -> n^2 - 1 / (n^3 + 6n) / (1/n) = (n^2)(n) / (n^3 + 6) then take lim n->∞ and plug in -> =1, which is above 0, so it diverges like 1/n. I don't get it. One method says it converges, the other says diverges. Which one do I use? Am I making a mistake? Please help me!