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Power Series

Definition

A power series is an infinite series that represents a function as an infinite polynomial expression.

Related terms

Radius of Convergence: The distance from the center point at which a power series converges to its original function.

Taylor Series Expansion: An approximation method that uses power series to represent functions around specific points.

Maclaurin Series Expansion: A special case of the Taylor series expansion where the center point is 0.

"Power Series" appears in:

Study guides (3)

AP Calculus AB/BC - 10.11 Finding Taylor Polynomial Approximations of Functions
AP Calculus AB/BC - 10.13 Radius and Interval of Convergence of Power Series
AP Calculus AB/BC - 10.15 Representing Functions as Power Series

Additional resources (1)

AP Calculus AB/BC - Unit 10 Overview: Infinite Series and Sequences

Practice Questions (6)

Which test can be used to determine the interval of convergence of a power series?
If the radius of convergence of a power series centered at 0 is 5, what can be said about the interval of convergence?
If a power series centered at 0 has a radius of convergence of 3, what can be said about the interval of convergence?
If a power series has a radius of convergence of 0, what can be said about the interval of convergence?
If the interval of convergence for a power series is (-1, 5), what can be said about the radius of convergence?
What is a power series?

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