The **sum** of two numbers is what we get when we add the two numbers together. This operation is called **summation**. There are a number of ways of writing sums, with the most common being:

- Addition ()
- Summation ()
- Computerization:

- Sum = 0
- For I = M to N
- Sum = Sum + X(I)
- Next I (in Visual BASIC)

## Sigma notation

**Sigma notation** is a mathematical notation to write long sums in a short way. Sigma notation uses the Greek letter Sigma (), and takes upper and lower **bounds** which tell us where the sum begins and where it ends. The lower bound usually has a variable (called the **index**, often denoted by , or ) along with a value, such as "". This tells us that the summation begins at 2, and goes up by 1 until it reaches the number on the top.

## Properties

## Applications

Sums are used to represent series and sequences. For example:

The geometric series of a repeating decimal can be represented in summation. For example:

The concept of an integral is a limit of sums, with the area under a curve being defined as:

## Related pages

- Nicholas J. Higham, "The accuracy of floating point summation",
*SIAM J. Scientific Computing***14**(4), 783–799 (1993).

*Kiddle Encyclopedia.*