Index of summation

Definition

The index of summation is the variable used to represent each term in a series as it is summed. Typically, it is denoted by symbols like $i$, $j$, or $k$ and appears in the notation of a series.

5 Must Know Facts For Your Next Test

1. The index of summation usually starts at a specified initial value and increments by 1 until it reaches its final value.
2. Changing the index of summation does not alter the sum if correctly adjusted.
3. Common choices for indices include $i$, $j$, and $k$, but any symbol can be used.
4. The index of summation must be consistent throughout the series expression.
5. It often appears in sigma notation, which compactly represents long sums.

Related terms

Sigma Notation: A concise way to express the sum of a series using the Greek letter $\Sigma$.

Series:

A sum of terms that follow a specific pattern.

Sequence:

An ordered list of numbers following some rule.