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Power Series

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A power series is a sum of powers of a variable. A power series is essentially an infinite polynomial.

Power series is a college-level concept that would be first encountered in a Calculus II course. It is an Advanced Placement Calculus BC topic and is listed in the California State Standards for Calculus.

Examples

Generating Function: The generating function of a sequence of numbers is a formal power series whose coefficients are the members of that sequence.
Geometric Series: A geometric series is a series in which the ratio of any two consecutive terms is always the same.
Taylor Series: A Taylor series is a power series of a function around a given point.

Prerequisites

Power: In arithmetic, a power is an exponent to which a given quantity is raised.
Series: In mathematics, a series is an (often infinite) sum of terms specified by some rule.

Classroom Articles on Calculus II (Up to College Level)

  • Arc Length
  • Maclaurin Series
  • Convergent Series
  • Radius of Convergence
  • Exponential Growth
  • Ratio Test
  • Harmonic Series
  • Surface of Revolution