[Coda]

The symbol is called "sigma" (it's an uppercase sigma, to be specific) and it represents "summation". An uppercase pi (Π) represents a product (that is, multiplication) used the same way.

The S_n notation is more general. You can use it to describe any sequence. It's also fairly common to use f(n) notation, especially for sequences that you want to find a continuous (in the sense of a continuous function) extension for.

The disadvantage of the more general notations is that they are also less useful. Summations and products have a number of very useful properties -- for example, Σkx = kΣx -- that do not hold for generalized sequences. (Note that this is true in general: the more generalized a form is, the fewer consistent properties that are available using it.)