4 videos in "Sequences and Series"
Power Series
Power Series
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Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Functions defined by power series. Ratio and root tests for absolute convergence. Differentiation and integration. Closed forms for series derived from geometric series. Series expansions of ln(1+x) and inverse tan (x).
- What is a power series?
- What is a power series about x0?
- What are variations on the geometric series?
- How can you find closed forms for power series?
- What is a radius of convergence?
- How do you find the radius of convergence of a power series?
- What is the interval of convergence?
- How do you find the interval of convergence for a power series?
- How do you take the derivative and interval of a power series?
- What is a power series expansion?
- What is the power series expansion of ln(1 + x)?
- What is the power series expansion of inverse tan x?
- What is the exact value of the sum of k^2/2^k?
Power series are defined and explained in depth in this lesson, as we are prepared for the final two lectures. The radius of convergence and interval of convergence are also defined, explained, and found for several different cases. Power series expansions are also found for several different functions.
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