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Series: Calculus: Power Series

About this Series

  • Lessons: 5
  • Total Time: 0h 51m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/29/2009
  • Last Updated At: 04/11/2011

In this 5-lesson series, we'll cover Power Series, Intervals of Convergence, and the Radius of Convergence. A power series is the infinite sum of successive powers of a given variable each accompanied by a coefficient. Power series are the generalization of Taylor and Maclaurin series. All power series converge for x = c. If a power series converges for any other values of x, then it converges for all x-values on an interval of convergence centered at x = c.

The interval of convergence of a power series is the collection of points for which the series converges. The radius of convergence of a power series is the distance between the center and either endpoint of the interval of convergence. We'll derive both of these concepts. Then, you'll learn to use the ratio test to find the radius and interval of convergence. We'll do this with several series, including x^n / n! and x^n / n and x^n * (x - 1)^n and (-1)^n (x-3)^n / (n*2^n) and (-x)^n / n^(1/2). Once we find the intervals and radius of convergence for each of these, we'll learn how to check our endpoints such that we can verify whether they are included in the interval or not.

For the next layer of information on Power Series, check out: the Power Series Function Representations series at:

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

2174 lessons

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Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

None of the lesson in this series have been reviewed.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: