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Math Help - Riemann Sums, Sparknotes version.

  1. #1
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    Riemann Sums, Sparknotes version.

    Ok, I am aware of how to do (not fluently) summations, but Riemann sums throw me off so much. So here is my best description:

    n
    \sum k^2
    i=1
    This turns to :
    n
    \sum f(i)
    i=1
    Where f(i)=i^2.

    Ok, I know n is the number of "rectangles" which will approach infinity. Your counter is i, which replaces k or x or whatever you use. How do I find c, and where does \Delta x come from? What do they mean? What is the difference between regular sums and Riemann sums? I am pretty quick to follow along, so feel free to be brief, I should be able to keep up. I also know most of the i \Rightarrow n conversions, e.g. c=cn, i^2= \frac {n(n+1)(2n+1)}{6} or whatever, I just need to figure out ci and \Delta x. I also have trouble figuring out riemann summations in general, a quick drive by of HOW to do them would be great, I already know why they work, I just can't make them work.
    Last edited by Thikr; May 4th 2010 at 06:59 PM.
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  2. #2
    Junior Member
    Joined
    Jan 2010
    Posts
    43
    How to Find Approximate Area Using Sigma Notation Video ? 5min.com

    Areas, Riemann Sums, and Definite Integrals Video ? 5min.com

    Calculus Videos
    (video's 21 to 23!)


    (and part two!).

    I think if you watch these videos in order you'll ace Riemann sums & understand everything perfectly.

    By the way, the sum you've shown is not a Riemann sum but it is a summation formula.

    There is a way to derive it but I suggest to you to first concentrate on understanding a Riemann sum & what it is then come back to tis forum to ask how to derive this formula.
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