# Summation Symbol

The capital letter Sigma Σ represents a summation or 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.

For example the summation from i = 1 to 3 of the expression i 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:

## Examples

### Summation

This example shows how the summation symbol works.

### Summation Using Variable i

This example shows a summation that uses the index variable in the expression.

### Summation of Elements in a Set

This example shows how the summation symbol can be used to sum elements within a set.

See also: