Does the following series converge or diverge?

\begin{equation}
 \sum^{\infty}\_{n=2} \left(\ln\left(\frac{n}{n-1}\right) - \frac{1}{n}\right)
\end{equation}

I have noticed that each of partial sum telescopes leaving me with:

\begin{equation}
S\_n = \ln(n) - \sum^{n}\_{k=2}\frac{1}{k}
\end{equation}

I know that harmonic series are divergent, I am not sure how to use that fact in this case though. How should one follow from here?