
Integral test
Posted:
Dec 10, 2012 4:05 PM


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 counterexample. Any ideas?
Best regards,
Jose Carlos Santos

