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Power Series Section 9.1. If the infinite series converges, then.

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Presentation on theme: "Power Series Section 9.1. If the infinite series converges, then."— Presentation transcript:

1 Power Series Section 9.1

2 If the infinite series converges, then

3 Geometric Series

4 Definition: Power Series An expression of the form is a power series centered at x=0. An expression of the form is a power series centered at x=a

5 Term-by-Term Differentiation converges for Then the series obtained by differentiating the series for f term-by- term, converges for and representson that interval.

6 Term-by-Term Integration converges for Then the series obtained by integrating the series for f term-by- term, converges for and represents on that interval.


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