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Calculus 2 - Infinite Series

  1. Nov 4, 2011 #1
    Determine weather or not the following series converges or diverges.

    sum[k=1,inf] 2/(k^2-1)

    I applied the limit comparison test with 1/k^2

    2* lim k->inf [ 1/(k^2-1) ] /(1/k^2) = 2*lim k->inf k^2/(k^2-1) =H 2

    then because

    sum[k=1,inf] 1/k^2 is a convergent p-series then sum[k=1,inf] 2/(k^2-1) must also converge by the limit comparison test.

    I plugged this into wolfram alpha and it said that the sum does not converge. Am I doing something wrong? Thanks for any help.

    This is what I put into wolfram alpha
    sum[n=1,inf] of 2/(k^2-1)
     
  2. jcsd
  3. Nov 4, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    Oh, I see what you are doing. Do you really mean [n=1,inf]?? n?? And the k=1 term of your series is undefined. Skip it.
     
  4. Nov 4, 2011 #3
    so I changed it to
    sum[k=1,inf] of 2/(k^2-1)
    and it says the sum does not converge
     
  5. Nov 4, 2011 #4

    Dick

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    Science Advisor
    Homework Helper

    I told you. The k=1 term is undefined. That's probably WA's problem with that one.
     
  6. Nov 4, 2011 #5
    Oh. Thanks.
     
  7. Nov 4, 2011 #6

    Mark44

    Staff: Mentor

    Might be a case of GIGO, or "garbage in, garbage out."
     
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