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Radius of Convergence

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The radius of convergence of a power series is half the width of the interval inside which it converges absolutely.

Radius of convergence 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.

Prerequisites

Power Series: A power series is a sum of powers of a variable. A power series is essentially an infinite polynomial.
Taylor Series: A Taylor series is a power series of a function around a given point.

Classroom Articles on Calculus II (Up to College Level)

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