Sigma - Is this right?

[Lizzie]

$\displaystyle \Sigma$ is only used in cases where you are trying to find the Riemann sum???

If this is true, then what does the stuff on the top and bottom mean? I never fully understood this.

 

[galactus]

Hey Lizzie:

No, the capital sigma is not used exclusively for Riemann sums. It is used in Riemann sums, though, because you're adding up a bunch of rectangle areas.

It is used to indicate summation from some point, say n=1, to some other point, maybe infinity, maybe something finite.

For instance, let's say we wanted to add up all the numbers from 1 to 100:

we could write this as:

$\displaystyle \sum_{n=0}^{100}n=1+2+3+4+....+100$

 

[Lizzie]

Thanks for your wonderful explanation! Unfortunatly, I have already failed... I uhm, I mean taken my Calculus exam. Looks like I'll be frequenting this site next semester as well.

 

[jolly]

Failed your exam? How bad was it?

 

[Lizzie1]

Well, out of two and a half pages of work and 10 problems with 2 hours to do them, I only FULLY understood the first page... That's how bad. My problem is that I got good grades in the first half of the semester because I already knew it before college, and then the second half I had to teach myself because it's an online course with NO interaction. That's where I started to fail and now I am going to have to retake Calculus. That's ok, tough because I wouldnt want to go on without fully understanding Calc. I'd just fail next year as well if I did that.