
Re: Integral test
Posted:
Dec 11, 2012 1:37 PM


On Mon, 10 Dec 2012 21:05:31 +0000, José Carlos Santos <jcsantos@fc.up.pt> wrote:
>Hi all, > >One of my students asked me today a question that I was unable to >answer. Let _f_ be an analytical function from (0,+oo) into [1,+oo) and >suppose that the integral of _f_ from 1 to +oo converges. Does it follow >that the series sum_n f(n) converges?
Certainly not.
> I don't think so, but I was unable >to find a counterexample. Any ideas?
sum_n (1 + (xn)^2)^{k(n)}
gives a counterexample if k(n) > infinity fast enough.
Details in a few days after finals are done, if you remind me...
> >Best regards, > >Jose Carlos Santos

