The summation operator is represented by the symbol (capital sigma) 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.
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.