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 ]
Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Re: Integral test
Posted: Dec 10, 2012 5:10 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 10-12-2012 21:34, Virgil 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?

> One can imagine an analytic function which is equal to 1 at every
> natural number but such that the sequence of its integrals from n-1/2 to
> n+1/2 converges.
> I do not have a concrete example in mind but I'm certain that it is
> possible.
> It could easily be derived from an analytic function with value 0
> outside [-0.5 , .5] and value 1 at 0.

Yes, but no such function exists.

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]

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