Determine the convergence of ∑n=1∞ln(n)n2\sum_{n=1}^{\infty} \frac{\ln(n)}{n^2}∑n=1∞n2ln(n).
Converges by Comparison Test with ∑1n1.5\sum \frac{1}{n^{1.5}}∑n1.51
Diverges by the Integral Test
Converges by the Alternating Series Test
Diverges by the Ratio Test