By the Integral Test, determine the convergence of ∑n=2∞lnnn2\sum_{n=2}^{\infty} \frac{\ln n}{n^2}∑n=2∞n2lnn.
Converges; ∫2∞lnxx2dx\int_2^{\infty} \frac{\ln x}{x^2} dx∫2∞x2lnxdx converges
Diverges; ∫2∞lnxx2dx\int_2^{\infty} \frac{\ln x}{x^2} dx∫2∞x2lnxdx diverges
The test is inconclusive
Diverges by the Divergence Test