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Does this series converge.

  1. Jan 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Does the series infinity n(sin(1/n)) converge?
    E
    n=1



    2. Relevant equations

    n

    and

    sin(1/n)



    3. The attempt at a solution

    The equation sin(1/n) looks familiar, maybe i could use the squeeze theorem?

    something like -1 <= sin(1/n) <= 1

    i'm not sure where to go after this though, or if i'm even on the right track?
    please help.
    thankyou.
     
  2. jcsd
  3. Jan 16, 2007 #2

    arildno

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    Dearly Missed

    First check:
    Does the general term go to zero as n goes to infinity?
     
  4. Jan 16, 2007 #3

    Gib Z

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    Yes You could use the squeeze theorem and get -|x|< sin(1/x) < |x|, but that doesn't seem the help you much. Do what arildno said, maybe a few other convergence tests, try using Taylor Series? I'd say it does, but can't show you right now.
     
  5. Jan 16, 2007 #4

    dextercioby

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    Since this is not an alternating series, then only answering the question posed by Arildno is enough to solve the problem.

    Daniel.
     
  6. Jan 16, 2007 #5
    There is a general formula: as x approaches 0, (sin x)/x approaches 1. So you can apply this in your question. Let n=1/x, then you modify the equation, then you will get the answer that the series diverge, since the series does not have a sum.
     
  7. Jan 16, 2007 #6
    read next post.
     
    Last edited: Jan 16, 2007
  8. Jan 16, 2007 #7
    yes. i would say as n goes to infinity, it approaches 0.
    the reasoning is because starting with small numbers it gets larger around .01745...

    don't know where to go from here.

    thanks for all the feedback, i found it all useful.
     
  9. Jan 16, 2007 #8
    Numbers at a certain point don't really tell you much about the behavior at infinity. Take the limit of the terms as n goes to infinity, if it isn't 0 what can you say about the series?
     
  10. Jan 17, 2007 #9
    that it diverges.
     
  11. Jan 17, 2007 #10
    yes it does
     
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