Rotwang
Posts:
1,655
From:
Swansea
Registered:
7/26/06
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Re: Integral test
Posted:
Dec 18, 2012 2:07 PM
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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 counter-example. 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@dont-email.me> contains a corrected (AFAIK) version.
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