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Math Help - Comparing Reimann to this Integral

  1. #1
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    Comparing Reimann to this Integral

    Given:
    n
    Sigma k/(n^2)
    k = 1

    show that
    limit as n-> infinity Sn = integral from 0 -> 1 on (xdx)
    by comparing the Reimann sum for the integral to the
    series.

    can someone walk me through this problem?, thanks
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  2. #2
    Senior Member
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    Apr 2009
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    Atlanta, GA
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    S= \int_0^1 xdx=\lim_{n\rightarrow\infty} \sum_{k=0}^n f(x_k)\Delta , where n\Delta=b-a=1 and x_k=k\Delta.

    S=\lim_{n\rightarrow\infty}  \sum_{k=0}^n k\Delta^2=\lim_{n\rightarrow\infty}  \sum_{k=0}^n \frac k{n^2}
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