The discussion revolves around the convergence or divergence of the series defined by the expression n = 1 to infinity of (n * sin(1/n)). Participants are exploring the nature of this series, particularly focusing on the behavior of the terms as n approaches infinity.
The discussion is active, with participants providing hints and questioning each other's reasoning. Some guidance has been offered regarding the comparison test and the importance of the limit of the terms in determining convergence. Multiple interpretations of the series' behavior are being explored.
There is some confusion regarding notation, specifically whether 'E' refers to a sigma notation. Additionally, participants are grappling with the implications of limits and the conditions for convergence, particularly the necessity for terms to approach zero.
No, you don't know that! You only know that the limit is 0.rcmango said:Homework Statement
n = 1 E infinity (n * sin (1/n))
Homework Equations
geometric series test?
The Attempt at a Solution
It looks like a geometric series.
i know that sin 1/n = 0 by squeeze theorem.
But none of your terms is n* 0 so that is irrelevant.n * 0 will always be 0.
No!am i on the right track, please help.
rcmango said:Okay, thanks Dick, you limit is 1.
i could use the comparison test, compare to 1/n
divide an / bn and get 1 by the nth term series. Thus diverging because it doesn't = 0.
thats what i made out of it. thanks a lot.