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 Petry

Posts: 1,104
Registered: 12/8/04
Re: Integral test
Posted: Dec 20, 2012 12:29 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Tuesday, December 18, 2012 6:30:09 PM UTC-8, david petry wrote:
> On Monday, December 10, 2012 1:05:31 PM UTC-8, José Carlos Santos 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?

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

That's not quite right because it's not analytic when cos(pi x) = 0

f(x) = ( cos(pi x)^2 + exp(-x) )^x^4 should work.

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

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.