

Summation of a series of numbers is frequently used in statistical and communication theory. A shorthand notation is used to represent a series of additions:
Σ (Sigma), used to denote "the sum of."
where the general form is:
For example:
represents the sum of the series X_{1} + X_{2} + X_{3} + ... X_{n}. To illustrate, if n = 4 and the series of numbers is {1, 2, 3, 4}, then this operation would produce the result 10. Note that the variable expression must be summed before any external operator can be applied; so for example:
This is clearly demonstrated using the previous example series {1, 2, 3, 4} and n = 4.
1^{2} + 2^{2} + 3^{2} + 4^{2} ≠ (1 + 2 + 3 + 4)^{2}
30 ≠ 100
Summation is frequently used with more complex variable expressions, such as summation of a series of products:
It is important to recognize here that the first instance of x is multiplied by the first instance of y and so on through the series. There are a number of other basic rules applicable to summation operations, these include:
Rule 1: The summation of the sum of two variables is equal to the sum of the two summations of those variables:
Rule 2: The summation of the subtraction of two variables is equal to the difference between the two summations of those variables:
Rule 3: The summation of a constant n times is equal to the product of n and that constant:
Rule 4: The summation of the product of a constant and a variable is equal to the product of the constant and the summation of that variable:

