Summation notation

Definition

Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of terms. It is denoted by the Greek letter sigma ($\Sigma$) followed by an expression that describes each term in the series.

5 Must Know Facts For Your Next Test

1. The general form of summation notation 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. If the upper limit $n$ is less than the lower limit $m$, then the summation yields zero.
3. $\sum_{i=1}^{n} c = nc$, where $c$ is a constant.
4. Summation properties include linearity: $\sum (a_i + b_i) = \sum a_i + \sum b_i$ and scalar multiplication: $\sum c \cdot a_i = c \cdot \sum a_i$.
5. Summation can be used to find arithmetic and geometric series sums.

Review Questions

• What does the expression $\sum_{i=1}^{5} i^2$ represent?
• How would you express the sum of the first n even numbers using summation notation?
• State and explain one property of summation notation.

Related terms

Arithmetic Series: A series in which each term increases by a constant difference. Represented as $a, a+d, a+2d,...$.

Geometric Series: A series in which each term increases by a constant ratio. Represented as $a, ar, ar^2,...$.

$\Sigma$ (Sigma): The Greek letter used to denote summation in mathematics.