Recent content by Banana Pie

Which of these converge? 1. 5n/ (2n-1) 2. e^n/ n 3. e^n/ (1+e^n) Attempt: 1) lim n-> ∞ 5n/(2n-1) = 5n/2n = 5/2 ≠ 0 so diverge? 2) Change n to x e^x/ (1 + e^x) Antiderivative: ln |1 + e^x| lim t->∞ of ln |1 + e^x| ln |1 + e^∞| - ln |1 + e^0| Got stuck here 3) Help :(

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)...