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