Summation notation

Definition

Summation notation is a mathematical way to represent the sum of a sequence of terms. It uses the Greek letter sigma (Σ) to indicate summation.

5 Must Know Facts For Your Next Test

1. The general form is $\sum_{i=m}^{n} a_i$, where $i$ is the index of summation, $m$ is the lower limit, and $n$ is the upper limit.
2. The expression $a_i$ represents the terms being added together.
3. If the upper limit is less than the lower limit, the summation equals zero by convention.
4. Summation notation can be used to simplify expressions involving series and sequences.
5. It is often used in calculus, statistics, and linear algebra for compact representation of sums.

Review Questions

• What does $\sum_{i=1}^{n} i$ represent?
• How would you expand $\sum_{k=2}^{5} (3k + 1)$?
• What happens if the upper limit is less than the lower limit in summation notation?

Related terms

Sequence:

An ordered list of numbers that follow a particular pattern or rule.

Series:

The sum of the terms of a sequence.

Index of Summation: A variable representing each term in a sequence within summation notation.