Power Series Section 9.1

If the infinite series converges, then

Geometric Series

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

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.

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.