Show that $\sum_{k=1}^\infty \frac{\ln{k}}{k^2}$ converges or diverges Show that $\sum_{k=1}^\infty \frac{\ln{k}}{k^2}$ converges or diverges


I know that I must use the Limit Comparison test and my instinct tells me that this series will converge. I cannot, however, think of another series $b_k$, to compare my given series to in order to show that it converges.

Any hints? 

Thank you!
Hint:

$$\sum_{k=1}^{\infty} \frac{\text{ln}\ k}{k^2} &lt; \int_{1}^{\infty}\frac{\text{ln}\ x}{x^2} dx = 1 $$
Equals the constant in http://oeis.org/A073002 , which gives further links.