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# Lesson 11.7: Sigma Notation

## Explanation

The symbol used for sigma is the capital Greek letter, s. In braille, this is a three-celled symbol with the Greek letter indicator, dots four six, in the first cell, the capitalization indicator, dot six, in the second cell, and the braille letter, s, in the third cell. The sign for sigma is usually displayed with other characters. In print, it may have mathematical characters or expressions below or above it, or superscripted or subscripted to its right on the baseline.

## Expressions directly under or directly over the Sigma

For material that is positioned directly under or over the sigma, the five-step rule for brailling modified expressions is used. Material that is directly under the sign for sigma is brailled first; this is usually an equation that shows the starting value for the summation. The material directly over the sign for sigma, the value where the summation ends, is brailled next. The sign for sigma is treated like a sign of operation; thus, it is unspaced from the expression related to it.

The multipurpose indicator is only used before the sign for sigma to show that it is being changed. When a numeral, variable, expression or other material is presented before the sign for sigma, the multipurpose indicator is not the first character on the line.

The first examples show the steps involved in writing properly formatted sigma notation.

### Example 1

a summation with a starting value of n equals one
⠐⠨⠠⠎⠩⠝⠀⠨⠅⠀⠼⠂

### Example 2

a summation with a starting value of n equals one and an ending value of nine
⠐⠨⠠⠎⠩⠝⠀⠨⠅⠀⠼⠂⠣⠔

### Example 3

a summation with a starting value of n equals one and an ending value of nine and five n on the baseline
⠐⠨⠠⠎⠩⠝⠀⠨⠅⠀⠼⠂⠣⠔⠻⠢⠝

### Example 4

a summation with a starting value of seven, an ending value of twenty, and two p plus one as the expression being used for consecutive sums.
⠐⠨⠠⠎⠩⠏⠀⠨⠅⠀⠼⠶⠣⠆⠴⠻⠆⠏⠬⠂

### Example 5

a summation with a starting value of one hundred, and ending value of one hundred fifty, and I squared as the expression being used for consecutive sums
⠐⠨⠠⠎⠩⠠⠊⠀⠨⠅⠀⠼⠂⠴⠴⠣⠂⠢⠴⠻⠠⠊⠘⠆

### Example 6

a complete summation with a starting value of one, and ending value of three, and 2t as the expression equals two open paren one close paren plus two open paren two close paren plus two open paren three close paren
⠐⠨⠠⠎⠩⠞⠀⠨⠅⠀⠼⠂⠣⠒⠻⠆⠞⠀⠨⠅⠀⠆⠷⠂⠾⠬⠆⠷⠆⠾⠬⠆⠷⠒⠾

### Example 7

two times the summation with a starting value of one, an ending value of three, and three r as the expression being used
⠼⠆⠐⠨⠠⠎⠩⠗⠀⠨⠅⠀⠼⠂⠣⠒⠻⠒⠗

### Example 8

a summation with a starting value of k equals one, an ending value of thirty, and open parenthesis four k plus 6 close parenthesis as the expression being used
⠐⠨⠠⠎⠩⠅⠀⠨⠅⠀⠼⠂⠣⠒⠴⠻⠷⠲⠅⠬⠖⠾