Discuss the convergence or divergence of the series .
By the Cauchy condensation test, we know that this series and the series
either both converge or both diverge. Looking at this new series, it is clear to see that it diverges.
The terms do not even go to 0 in this series, so by the nth term test, it diverges. Thus, by the Cauchy condensation test, it is also true that our series diverges.