Summation Notation


The capital letter Sigma Σ represents the summation operation in mathematics, often called sum for short. A sum has three parts: an initial value, an end value, and the expression being summed. The summation starts at the initial value and iterates, adding one to the value for each iteration, stopping when the value reaches the end value.

Summation Notation Annotated

For example, the summation from i = 1 to 3 of the expression shown below is equal to one plus two plus three. Since the expression being summed is the variable i, then i starts at one, iterates to two, iterates to three, and then stops there since it is the ending value:


To calculate the summation of the counting numbers 1 + 2 + 3 + ... + n the sequence can be visualized geometrically and solved for by finding the area of the shape formed.