Sigma notation

Definition

Sigma notation, also known as summation notation, is a way to represent the sum of a sequence of terms. It uses the Greek letter sigma ($\sum$) to indicate that a series of terms should be added together.

5 Must Know Facts For Your Next Test

1. Sigma notation is commonly used to express the sum of a finite or infinite sequence.
2. The general form is $\sum_{i=a}^{b} f(i)$, where $i$ is the index of summation, $a$ is the lower bound, and $b$ is the upper bound.
3. It simplifies expressions involving large sums and makes it easier to write them compactly.
4. In integration, sigma notation can be used to approximate areas under curves through Riemann sums.
5. The limits of summation can change depending on whether you're dealing with definite or indefinite sums.

Review Questions

• What does the index of summation represent in sigma notation?
• How would you write the sum of squares from 1 to n using sigma notation?
• Explain how sigma notation can be used in approximating areas under curves.

Related terms

Riemann Sum: A method for approximating the total area underneath a curve by dividing it into shapes (typically rectangles) and summing their areas.

Definite Integral: Represents the exact area under a curve between two points. It can be thought of as the limit of a Riemann sum as the number of subdivisions approaches infinity.

Sequence: An ordered list of numbers that often follows a specific pattern or function.