
Re: Integral test
Posted:
Dec 12, 2012 11:49 AM


On Tue, 11 Dec 2012 22:48:14 +0000, George Cornelius <gcornelius@charter.net> wrote:
>David C. Ullrich wrote: >> 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. > >Missing a negative sign before the k(n) ?
Yes, sorry.
> >Similar would be a sum of bell curves, > > sum_n exp((xn)^2 k(n)) , > >where k(n) is, say, n^4 . > >> Details in a few days after finals are done, if you remind me... >> >>> Best regards, >>> >>> Jose Carlos Santos

