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Need to find a convergent value

  1. Oct 15, 2005 #1
    Given this sum

    [tex] s = \sum_{k = 1}^{{\frac{x}{j}} - 1} k^{n}j^{n+1}[/tex]

    x and n are constants

    and x/j is a positive integrer and k is an integrer

    To what value s converges as

    [tex]{j}{\rightarrow}{0}[/tex]
    ?

    Edit: I have found that the awnser is [tex]\frac{x^{n+1}}{n+1}[/tex], but i do not know how to obtain this...
     
    Last edited: Oct 15, 2005
  2. jcsd
  3. Oct 16, 2005 #2
    What do you recognize if I write
    [tex]s = \sum_{k=1}^{N-1} x_k^n \Delta x[/tex]
    where [tex]N = x/(\Delta x)[/tex] and [tex]x_k = k \Delta x[/tex]? What about a Riemann sum?
     
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