Sigma

Definition

Sigma ($\Sigma$) is a mathematical notation used to represent the sum of a sequence of terms. It is often used to succinctly express the addition of series, especially in algebra and trigonometry.

5 Must Know Facts For Your Next Test

1. The sigma notation $\Sigma$ is followed by an expression that defines the terms to be added.
2. $\Sigma_{i=1}^{n} a_i$ means summing the terms $a_i$ from $i=1$ to $i=n$.
3. In finite series, the upper limit of summation (n) indicates how many terms are included in the sum.
4. Sigma notation can be used for arithmetic and geometric series.
5. Simplification rules for sigma notation include properties like linearity: $\Sigma (a + b) = \Sigma a + \Sigma b$.

Review Questions

• How do you write the sum of integers from 1 to n using sigma notation?
• What does $\Sigma_{k=1}^{5} k^2$ represent?
• Explain how you would simplify $\Sigma_{j=1}^{4} (2j + 3)$.

Related terms

Arithmetic Series: A sequence of numbers in which the difference between consecutive terms is constant.

Geometric Series: A sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio.

Summation: The process of adding a sequence of numbers; also represented by sigma notation.