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Evaluating an Infinite Series (non geometric)

  1. May 3, 2010 #1
    1. The problem statement, all variables and given/known data


    lim n-> infinity of Sum (from k = 1 to n) of sqrt(k/n) * 1/n

    2. Relevant equations
    taylor series?

    3. The attempt at a solution
    the above = lim n->infinity of Sum (from k = 1 to n) of k^1/2 / n^3/2
    k approaches n so
    n^1/2 / n^3/2 -> 1/n -> diverge

    correct answer is 2/3 i have no idae how to get it help
  2. jcsd
  3. May 3, 2010 #2
    Your sum is the approximation of an integral of a certain function from 0 to 1 with n values. If n->inf then the limit of the approximation becomes is the integral.
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