Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Proof Sum_Integral Date
B Proof of a limit rule Dec 19, 2017
B Proof of quotient rule using Leibniz differentials Jun 10, 2017
B Don't follow one small step in proof Jun 10, 2017