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Express sum as a definite integral

  1. Feb 2, 2012 #1
    The problem statement, all variables and given/known data

    If n is a positive integer, then
    [tex]\lim_{n\to\infty}\frac{1}{n}\left[\left(\frac{1}{n}\right)^2+\left(\frac{2}{n}\right)^2+\cdot\cdot\cdot+\left(\frac{n-1}{n}\right)^2\right][/tex]can be expressed by what definite integral?

    The attempt at a solution

    A student I was helping had this problem and I had no idea how to even start. It was a problem along with other basic calc I definite and indefinite integrals, so I'm guessing it has some easy solution that I'm completely missing.
     
  2. jcsd
  3. Feb 2, 2012 #2

    Dick

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    You don't know Riemann sums as approximations to integrals??
     
  4. Feb 2, 2012 #3
    I knew it was something simple :rolleyes:
    Makes sense; now I just need to figure out f(x)...
     
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