Sum

The sum of two numbers is their value added together. This operation is called additive summation or addition. There are many ways of writing sums, including:
Addition ()
Summation ()
Code:
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:

Calculating the mean of a set of numbers can be expressed like this, where each  can be any number.

So, because , you could also calculate the mean like  as well.

 Related pages 

 Product (mathematics)

 References 

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

Other websites

 Sigma Notation  on PlanetMath
 Derivation of Polynomials to Express the Sum of Natural Numbers with Exponents 

Category:Arithmetics
Category:Mathematical notation