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Representation of Functions by Power Series

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1 Representation of Functions by Power Series
Lesson 9.9

2 Geometric Power Series
Consider the function Note the similarity to the sum of the geometric series

3 Geometric Power Series
Thus we could let a = 1 and r = x and have Where is this power series centered? At x = 0, for the interval -1 < x < 1 Note also that our original f(x) is defined for all x ≠ 1

4 Geometric Power Series
To center this series at x = -3 you could specify Then a = ¼ r = [(x + 3)/4] So convergence would be for the interval

5 Geometric Power Series
Try this out … find a power series for the function centered at c

6 Operations with Power Series
Note the following rules

7 Adding Two Power Series
Consider a function which can be broken into two using partial fractions Now determine two geometric power series which are added to give us a series for the original function

8 Try Another Try these … just for practice See Example 4 and Example 2

9 Assignment Lesson 9.9 Page 674 Exercises 5 – 25 odd


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