Determine whether the series converges or diverges.
Summation of (ln(k))/(k^3)
Oh sure it converges. This is because $\displaystyle \frac{\ln k}{k^3}=\frac{\ln k}{k}\cdot\frac{1}{k^2}$, where the first factor $\displaystyle \frac{\ln k}{k}$ converges to $\displaystyle 0$ for $\displaystyle k\to\infty$ and the series $\displaystyle \sum_k \frac{1}{k^2}$ of the second factor $\displaystyle \frac{1}{k^2}$ also converges. - But maybe this way of arguing for convergence is a little too sloppy for your taste.