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Topic: Integral test
Replies: 17   Last Post: Dec 20, 2012 12:29 PM

 Messages: [ Previous | Next ]
 David Petry Posts: 1,104 Registered: 12/8/04
Re: Integral test
Posted: Dec 18, 2012 9:30 PM

On Monday, December 10, 2012 1:05:31 PM UTC-8, José Carlos Santos 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? I don't think so, but I was unable
>
> to find a counter-example. Any ideas?

how about f(x) = (cos(pi x)^2)^x^4

Date Subject Author
12/10/12 Jose Carlos Santos
12/10/12 Virgil
12/10/12 Jose Carlos Santos
12/10/12 Butch Malahide
12/11/12 Jose Carlos Santos
12/11/12 RGVickson@shaw.ca
12/10/12 Leon Aigret
12/10/12 Rotwang
12/11/12 Jose Carlos Santos
12/18/12 Phil Carmody
12/18/12 Rotwang
12/11/12 Rotwang
12/11/12 David C. Ullrich
12/11/12 George Cornelius
12/12/12 David C. Ullrich
12/18/12 David Petry
12/20/12 David Petry