# Calc6.64

From Example Problems

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.