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Lecture

# 11.8 Power Series Question #1 (Easy)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
11.8 Infinite Sequences & Series Power Series Question #1 (Easy): Determining the Radius and Interval of Convergence Strategy Power series contain variable in the series expression so that ∑ where ’s are coefficients and is a variable. Power series looks like polynomial, except with infinite terms. Sometimes restrictions apply to the possible values that can take to make the power series convergent. Ratio test can be used to determine this radius for the series convergence. Then various series tests learned so far can apply to be more specific about the interval of convergence. Sample Question Find the radius of convergence and interval of convergence of the series. ∑ Solution Notice that the series contains a variable x. Thus, the range of values that x can take which makes the series convergent need to be determined. In order to do so, first put into the ratio test and get the outcome of the ratio test which will contain the variable x. Then the value of x can be determined which will make outcome of the ratio test to be less than 1. Then and ( ) . The ratio test: | | | | | ( ) ( ) |
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