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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

$\sum _{n=1}$
⠐⠨⠠⠎⠩⠝⠀⠨⠅⠀⠼⠂

### Example 2

$\sum _{n=1}^{9}$
⠐⠨⠠⠎⠩⠝⠀⠨⠅⠀⠼⠂⠣⠔

### Example 3

$\sum _{n=1}^{9}5n$
⠐⠨⠠⠎⠩⠝⠀⠨⠅⠀⠼⠂⠣⠔⠻⠢⠝

### Example 4

$\sum _{p=7}^{20}2p+1$
⠐⠨⠠⠎⠩⠏⠀⠨⠅⠀⠼⠶⠣⠆⠴⠻⠆⠏⠬⠂

### Example 5

$\sum _{I=100}^{150}{I}^{2}$
⠐⠨⠠⠎⠩⠠⠊⠀⠨⠅⠀⠼⠂⠴⠴⠣⠂⠢⠴⠻⠠⠊⠘⠆

### Example 6

$\sum _{t=1}^{3}2t=2\left(1\right)+2\left(2\right)+2\left(3\right)$
⠐⠨⠠⠎⠩⠞⠀⠨⠅⠀⠼⠂⠣⠒⠻⠆⠞⠀⠨⠅⠀⠆⠷⠂⠾⠬⠆⠷⠆⠾⠬⠆⠷⠒⠾

### Example 7

$2\sum _{r=1}^{3}3r$
⠼⠆⠐⠨⠠⠎⠩⠗⠀⠨⠅⠀⠼⠂⠣⠒⠻⠒⠗

### Example 8

$\sum _{k=1}^{30}\left(4k+6\right)$
⠐⠨⠠⠎⠩⠅⠀⠨⠅⠀⠼⠂⠣⠒⠴⠻⠷⠲⠅⠬⠖⠾