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

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

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David Petry

Posts: 1,046
Registered: 12/8/04
Re: Integral test
Posted: Dec 20, 2012 12:29 PM
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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.

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