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

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David Petry

Posts: 1,104
Registered: 12/8/04
Re: Integral test
Posted: Dec 18, 2012 9:30 PM
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On Monday, December 10, 2012 1:05:31 PM UTC-8, José 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?

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

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