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.
| Notation | |
|---|---|
\prod_{i=0}^{2}\left(i+1\right) |