Rotwang
Posts:
1,684
From:
Swansea
Registered:
7/26/06


Re: Integral test
Posted:
Dec 18, 2012 2:07 PM


On 18/12/2012 09:42, Phil Carmody wrote: > José Carlos Santos <jcsantos@fc.up.pt> writes: >> On 11/12/2012 00:57, Rotwang wrote: >> >>>> 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? I don't think so, but I was unable >>>> to find a counterexample. Any ideas? >>> >>> (I'm assuming you mean [0, +oo) instead of [1, +oo).) >>> >>> [wrong stuff snipped] >> >> Thanks. I will check the details. > > Well, it's not into, for a start.
I don't think "into" was supposed to mean injective, since otherwise the question is trivial even after [1, +oo) is corrected to [0, +oo). My original answer was wrong anyway though. Message <ka7rjr$5e3$1@dontemail.me> contains a corrected (AFAIK) version.
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