Testing convergence of $\sum\limits_{n=2}^{\infty} \frac{\cos{\log{n}}}{n \cdot \log{n}}$

This problem appears in the Nordic university-level mathematics team-competition, NMC, 2010, with solution at the beginning of the following pdf: http://cc.oulu.fi/~phasto/competition/2010/solutions2010.pdf.

The search was series "cos(log(n))".