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Homework Help: Riemann sum/limit question

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Find limn->∞ (1/n)(Ʃk=1 to n ln(2n/(n+k)))

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure if this is even a riemann sum at all, but I don't see what else it could be. I wanted to find the riemann portion first to get rid of the sigma notation then find the limit of everything, but I don't have any of the information I need to do the riemann sum or to convert it to an integral.
  2. jcsd
  3. Apr 16, 2012 #2
    I realize I need to be able to put it in a form of (b-a)/n Ʃ (a+(b-a)k/n), but I'm not sure how I can work with ln and manipulate it when everything is stuck in ln. Any tips?
  4. Apr 16, 2012 #3


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    Science Advisor
    Homework Helper

    If you can put it in the form of sum (1/n)f(k/n) for some function f then it's a Riemann sum of the function f(x) for x=0 to 1. What's f?
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