Calculus series help.?

Question

Determine whether or not the series converges or diverges. Any test is accepted.

∑ (infinity on top; n=1 on bottom) times (3n^3/2n+1)^n.....the total problem is raised to the "n" power.

Answer 1

Well, as n--> oo, 3n^3/(2n+1) --> oo and (3n^3/(2n+1))^n --> oo. Since a necessary condition for convergence is that the general term converge to 0, it follows this series diverges to oo.