
Re: Integral test
Posted:
Dec 20, 2012 12:29 PM


On Tuesday, December 18, 2012 6:30:09 PM UTC8, david petry wrote: > On Monday, December 10, 2012 1:05:31 PM UTC8, 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 counterexample. 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.

