Notation: The **Summation and Product Symbols** An oversized Greek capital letter sigma is often used to denote a summation, as in *Pn i=1 i.* This particular expression represents the sum of the **integers **from 1 to n; that is, it stands for the sum *1 + 2 + 3 + · · · + n.* More generally, we can sum any function f(i) of the summation index i. (Of course, the index could be some symbol other than i.) The expression Pb i=a f(i) stands for *f(a) + f(a + 1) + f(a + 2) + · · · + f(b)*

For example, *Pm j=2 j 2 stands for the sum 4 + 9 + 16 + · · · + m2 .* Here, the function f is **“squaring**,**”** and we used index j instead of i. As a special case, if b < a, then there are no terms in the sum *Pb i=a f(i),* and the value of the expression, by convention, is taken to be 0. *If b = a, then there is exactly one term, that for i = a. Thus, the value of the sum Pa i=a f(i) is just f(a).*

The** analogous notation** for products uses an oversized capital pi. The expression *Qb i=a f(i)* stands for the product *f(a) × f(a + 1) × f(a + 2) × · · · × f(b); if b < a,* the product is taken to be 1.