The summation operator is represented by the symbol (summation) and represents the operation of summing a sequence of expressions together. For example, the statement below represents the summation of the sequence of three numbers.
In plain language, this means: sum the sequence of numbers together represented by the expression 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 summation operator, in this case , controls the length of the sequence being multiplied. Expanding the expressions as a summation gives the following.
Adding together the sequence of expressions gives the result.