1. Section 12.8 Power Series
AP Calculus
March 25, 2010
CASA

2. Calculus, Section 12.8, Todd Fadoir, CASA, 2005
Power Series
A power series is a series in the form:
We use “c” because they act like coefficients; it looks to be an infinitely long polynomial.
Calculus, Section 12.8, Todd Fadoir, CASA, 2005

3. Power Series Centered at a
A power series centered at a is the form:
Because of this distinction, we sometimes call
a power series centered at zero
Calculus, Section 12.8, Todd Fadoir, CASA, 2005

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Insight
Power Series are always convergent at their “center”
Why?
Calculus, Section 12.8, Todd Fadoir, CASA, 2005

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Theorem
Power Series is always convergent in one of three ways
Only at the “center” (x=a)
For all values x=(-∞,∞)
There is some R (called the radius of convergence) that creates an interval of convergence (a-R,a+R). The series may or may not be convergent at the endpoints.
Calculus, Section 12.8, Todd Fadoir, CASA, 2005

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Assignment
12.8: 1-27 odd
Calculus, Section 12.8, Todd Fadoir, CASA, 2005