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Math Help - limit of sum

  1. #1
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    limit of sum

    \sum_{i=0}^n\frac{4}{n}*({1+(i/4n)})^4\

    as n goes infinite
    Last edited by chialin4; February 12th 2010 at 06:03 AM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Note that the sum is the Riemann Sum of f(x) = (1+x/16)^4

    on the interval 0 to 4

    So the sum = integral[(1+x/16)^4dx] from 0 to 4
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    Note that the sum is the Riemann Sum of f(x) = (1+x/16)^4

    on the interval 0 to 4

    So the sum = integral[(1+x/16)^4dx] from 0 to 4
    i think the interval is 1 to 5?? is it right??
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  4. #4
    MHF Contributor Calculus26's Avatar
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    No it is 0 to 4 see the attachment where I use mathcad to evaluate the sum and the integral to verify my results.

    Why do you think the interval would be 1 to 5 ?
    Attached Thumbnails Attached Thumbnails limit of sum-integral.jpg  
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