Power Series
Definition
A power series is an infinite series that represents a function as an infinite polynomial expression.
Analogy
Think of power series like different flavors of ice cream. Each flavor represents a different function, and when combined together (added infinitely), they create unique combinations or representations for various functions.
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)
Additional resources (1)
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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