Discuss the convergence or divergence of the series .
In this problem, we will use the Cauchy condensation test in the opposite direction that we have been using it. This series is already in the form
which we get by a bit of simplification, or perhaps complication.
Thus, this series converges or diverges with the series
This series converges because it is a p-series with p>1. Thus, our original series also converges.