Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: Integral test
Posted: Dec 11, 2012 1:37 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 counter-example. Any ideas?


sum_n (1 + (x-n)^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





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.