Date: Dec 10, 2012 4:05 PM Author: Jose Carlos Santos Subject: Integral test 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?

Best regards,

Jose Carlos Santos