Talk:Carleman's inequality

Proof given of equality condition seems incorrect

The inequality is established by applying AM-GM and other estimates to finitely many reals, and taking the limit for an infinite sequence. However, the equality condition does not necessarily transfer (not true that $\lim a=\lim b$ implies $a_{i}=b_{i}\forall i$.) Thus, AM-GM alone can't show that the inequality is strict for a convergent series.

Riemannzeta5 (talk) 01:59, 12 June 2020 (UTC)