Have you read this?
Hi;
Can somebody please provide me with an example of using the Cauchy condensation test (criterion " ") in checking convergence of series? I've never used it myself, and I'd really like to see a real example of application (it seems rather rare to use this criterion), not just the rule. I'd like to know how it works in practice.
Thanks for your time.
I suppose that you already know that is a convergent series iff is a convergent series. The Cauchy Condensation test can mainly be used to prove divergence for various series and we can firstly use this to prove the divergence of the harmonic series
Notice how
transforms to
under the Cauchy condensation test and hence diverges
I very much hope that that helps,
Paul