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Numerical Analysis - Summation/Integrals

  1. Dec 11, 2011 #1
    This is not so much of a homework problem but a practice problem for our final.

    Any advice or insight on how to approach this problem would be incredibly helpful!
    (Btw, I don't expect anyone to solve this for me, just want to make that clear! )



    Prove that:

    limit(n→∞) [ (1/n) * k=0Ʃ(n-1) (e^(k*x/n)) ] = (e^x - 1)/x , x > 0




    Honestly, I don't even know where to begin this problem. My professor gave us "hints" as to how to solve it.

    "Interpret the integral as a limit of sums"

    I need to somehow get to the integral:

    1
    ∫ e^(tx) dt
    0


    Thanks!
     
  2. jcsd
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