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Math Help - Riemman Sum

  1. #1
    Junior Member
    Joined
    Jan 2009
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    Riemman Sum

    The limit as x approches infinity of the sum from i=1 to n of :

    (1+\frac{i}{n})^3
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  2. #2
    Senior Member
    Joined
    Apr 2009
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    Atlanta, GA
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    408

    Divergent

    \lim_{n\rightarrow\infty}\sum_{i=1}^n(1+\frac{i}{n  })^3 = \lim_{n\rightarrow\infty}\sum_{i=1}^n\frac1{n^3}(n  ^3+3n^2i+3ni^2+i^3)= \lim_{n\rightarrow\infty} 1+\frac3n\sum_{i=1}^ni+\frac3{n^2}\sum_{i=1}^ni^2+  \frac3{n^3}\sum_{i=1}^ni^3 = \lim_{n\rightarrow\infty} 1+\frac3n\frac{n(n+1)}2+\frac3{n^2}\frac{n(n+1)(2n  +1)}6+\frac3{n^3}\frac{n^2(n+1)^2}4 = \infty

    This limit diverges. What was the original problem?
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