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Converge or diverge

  1. Jan 23, 2007 #1
    1. The problem statement, all variables and given/known data

    question is if this series converge absolutely, converge conditionally, or it diverges?

    here it is: http://img442.imageshack.us/img442/5899/untitled8tn.jpg
    2. Relevant equations


    3. The attempt at a solution

    not sure where to start, maybe with the limit comparison test or ratio test?
    please help. thanks.
  2. jcsd
  3. Jan 23, 2007 #2

    Gib Z

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    Homework Helper

    [tex]\sum_{n=1}^{\infinity} -1^n \cos \frac{1}{n}[/tex]. First check if the limit at infinity is less than 1. If each term is more than 1, it won't converge. So as we take the limit, Cos 0, its equal to 1. Since its 1, it diverges. So it can't be absolutely convergent.

    For an alternating series, the last term has to converge to zero as well, so its divergent as well.
    Last edited: Jan 23, 2007
  4. Jan 24, 2007 #3
    thanks for your help.
  5. Jan 24, 2007 #4

    Gib Z

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    Homework Helper

    No problemo :)
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