Talk:Cauchy condensation test

The proof could be clearer (I think)
In the proof of the theorem inequalities between infinite series are used. Since the convergence of at least one of the series involved in the inequality is not proved, I'm not sure one could do that (use the inequalities). It would probably be more cautious to define two sequences, each with elements corresponding to partial sums of each series. The sequences are both increasing (the elements of the series are positive). Now one series is assumed to be convergent, so its corresponding sequence is necessarily bounded. All that is left to do is to prove that this implies that the other sequence is also bounded, and therefore convergent (because it is also increasing). All of this can be done by comparing partial sums only. — Preceding unsigned comment added by 178.192.76.124 (talk) 19:46, 24 April 2013 (UTC)