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Homework Help: Show that a series converges

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data
    The series is at http://img203.imageshack.us/i/snapshot1g.png/

    3. The attempt at a solution

    The LHS series diverges. However, the term 1/n seems to be make the series to converge.
    However, I am not completely sure how to proceed in proving that the series converges.

    I should first show that the series has a converging point.
    Then I can show that the series converges.
  2. jcsd
  3. Feb 11, 2010 #2


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    That isn't a series, it is a sequence.

    [tex]a_n = \frac 1 n\left(\frac 1 2 + \frac 2 3 + ... + \frac n {n+1}\right)[/tex]

    One way to prove a sequence converges is to show it is bounded above and increasing. Try that.
  4. Feb 12, 2010 #3
    Its a riemann sum.
  5. Feb 12, 2010 #4
    ^ Clever! I missed the obvious.

    [/thread hijack]
  6. Feb 12, 2010 #5


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    I don't think it's really a Riemann sum. The kth term is (k/n)/(k+1). If it were a Riemann sum, that would be a function only of (k/n).
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