# Product Notation

The product operator is represented by the (capital pi) symbol and is used to represent the operation of multiplying a sequence of expressions together. For example, the statement below represents the product of a sequence of three numbers.

In plain language, this means multiply the sequence of expressions together represented by starting from and iterating until . At each step, the element of the sequence is calculated by substituting the current value of into the expression. The sequence of expressions is shown below.

Expression Variable

The expression on top of the product operator, in this case , controls the length of the sequence being multiplied. Expanding the expressions as a product gives the following.

Multiplying the expression together gives the result.