## series converges or diverges?

1. The problem statement, all variables and given/known data

n = 1 E infinity (n * sin (1/n))

2. Relevant equations

geometric series test?

3. The attempt at a solution

It looks like a geometric series.

i know that sin 1/n = 0 by squeeze theorem.

n * 0 will always be 0.

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 Recognitions: Homework Help Science Advisor rcmango, you really have to work on your notation. Is the 'E' supposed to be a sigma? If so then the nth term of your series tends to one. Can it converge?
 Hint: try applying your logic to n/n.

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## series converges or diverges?

 Quote by rcmango 1. The problem statement, all variables and given/known data n = 1 E infinity (n * sin (1/n)) 2. Relevant equations geometric series test? 3. The attempt at a solution It looks like a geometric series. i know that sin 1/n = 0 by squeeze theorem.
No, you don't know that! You only know that the limit is 0.

 n * 0 will always be 0.
But none of your terms is n* 0 so that is irrelevant.

No!
 Okay, thanks Dick, ya 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 alot.

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