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Proof of a Sum_Integral

  1. Jun 23, 2010 #1
    Can anybody help me with the following:

    [tex]\lim_{n \rightarrow \infty} = \frac{1^k+2+k+...+n^k}{n^{k+1}}=\frac{1}{k+1}[\tex]

    How do you proof this equation with the Riemann-integral, especially with upper/lower riemann sums?

    thank you!
  2. jcsd
  3. Jun 23, 2010 #2


    Staff: Mentor

    Just some help with your LaTeX...
  4. Jun 23, 2010 #3
    Find a particular integral so that the fraction on the left-hand-side is the Riemann sum when the interval is divided into n equal parts. Then that limit is the value of the integral.
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