Sigma Notation

Sigma notation, also known as summation notation, is a compact way of expressing addition. This notation consists of four parts.

1. The Greek letter sigma Σ. This letter indicates that the terms are added together.
2. The general form of all the terms being added, in terms of a variable. The variables n and i are commonly used.
3. The summation index and the starting index, also called the lower limit. They are placed below the letter sigma and are connected with an equals sign. The summation index is the variable used in the general form of the terms. The starting index is the first value that the variable takes.
4. The final index or upper limit. This number is placed above the letter sigma and indicates the value for the variable in the last term of the summation.

In the example below, all four parts are shown.

The variable n — the summation index — only takes integer values. To write this sum explicitly, the variable n must be replaced with the integers from the initial value through the final value. ∑_(n= 1)^4 2n &= 2( 1_(n= 1)) + 2( 2_(n= 2)) + 2( 3_(n= 3))+2( 4_(n= 4)) [1.5em] ∑_(n=1)^4 2n &= 0.26cm2 0.26cm+ 0.26cm4 0.26cm+ 0.26cm6 0.26cm+ 0.26cm8 0.1cm [1.5em] ∑_(n=1)^4 2n &= 20