I realize that, to some people, this is going to be trivial, but I would really like to understand the various different notations used in the math world. And, right now, my question is on Sigma(sum) notation and Pi(product) notation. Most specifically, in the equations:

and

I am curious what the

and the

in both examples means, exactly. I understand the symbols, and I know how to evaluate, but I just want to know the more intricate things that the notation means and, more specifically, how that leads to me being able to manipulate the notation to be more useful to me. Any help would be much appreciated.

Oh, and one more thing I'm curious about, if I wanted to us Pi notation where I have a sequence of

numbers denoted as

but I want to exclude one of those elements of

like, say

where

. Would this be represented as

or would it be