The Math Forum

Search All of the Math Forum:

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

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 ]
Leon Aigret

Posts: 31
Registered: 12/2/12
Re: Integral test
Posted: Dec 10, 2012 6:56 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mon, 10 Dec 2012 23:51:20 GMT, aigret.not@myrealbox.invalid (Leon
Aigret) wrote:

>On Mon, 10 Dec 2012 21:05:31 +0000,
>=?ISO-8859-1?Q?Jos=E9_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?

>If ïnto" means injectivity then the answer must obviously be yes
>because _f_ is monotonous. Otherwise, f(x) = cos (pi x^2) should work
>if absolute convergence of the integral is not required.

... and tried to concel it one minute later. Please ignore.


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

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.