# Definition:Summation/Index Variable

## Definition

Consider the summation, in either of the three forms:

$\displaystyle \sum_{j \mathop = 1}^n a_j \qquad \sum_{1 \mathop \le j \mathop \le n} a_j \qquad \sum_{\map R j} a_j$

The variable $j$, an example of a bound variable, is known as the index variable of the summation.

## Also known as

The index variable can also be seen referred to as dummy variable or dummy index.