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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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Jose Carlos Santos

Posts: 4,863
Registered: 12/4/04
Integral test
Posted: Dec 10, 2012 4:05 PM
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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

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