C.1. Sum Notation

Sums can be concisely written using the upper-case Greek letter sigma. For example,

is read, "The sum, for i from 1 to 4, of 2i2." This is:

Often the upper limit of the index (written above the sigma) is some other variable involved in the analysis, such as n. For example, in Section C.3, we will see a formula for the sum of the first n positive integers:

In order to wrangle an expression into a form for which we have a formula, it is often useful to add or remove terms. For example:

Substitution of variables is another useful technique. For example, to evaluate the sum

we define n = 2m. Then:

Sum notation is sometimes used more casually. For example, to describe the total value of all of the cars on a sales lot, we might write: