Riemann Sums, Sparknotes version.

**Thikr** · May 4th 2010, 06:46 PM

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.

**sponsoredwalk** · May 4th 2010, 08:09 PM

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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