Series converges or diverges?

  • Thread starter rcmango
  • Start date
  • #1
234
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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.

n * 0 will always be 0.

am i on the right track, please help.
 
Last edited:

Answers and Replies

  • #2
Dick
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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?
 
  • #3
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Hint: try applying your logic to n/n.
 
  • #4
HallsofIvy
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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.
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.

am i on the right track, please help.
No!
 
  • #5
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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.
 
  • #6
Dick
Science Advisor
Homework Helper
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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.

Pretty good. Except a ratio test giving you a limit of one doesn't tell you much. You could do a comparison with 1/n, that works. But it's still overkill. If the nth term of a series doesn't approach zero then it doesn't converge. Period. Ever.
 

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