Calculus Infinite Series Problem

Does it converge or diverge?

∞ . . . . NlnN
∑ . . . -----------
N=1 . . . N^2

I tried the Nth term test, but the limit equals zero, so I can't prove divergence.

Using the integral test, note that
∫(1 to ∞) x ln x dx/x^2
= ∫(1 to ∞) ln x dx/x
= (ln x)^2/2 {for x = 1 to ∞}
= ∞.

Hence, the sum in question must also diverge.

I hope this helps!