The product operator is represented by the (product) 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.
Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.
The summation operator is represented by the summation symbol ∑ and represents the operation of summing a sequence of expressions together.