1. S ECT. 9-3 P OWER S ERIES Sect. 9-8 in textbook

2. Power Series A series with variable terms like Is called a power series. Note that this series is a geometric power series. If it converges, the variable x must be

3. The Interval of Convergence

4. Power Series 1. For these x-values of this Geometric Power series This means for these x-values, the function can be written as

5. Power Series General Form A power series is a series of the form where x is a variable and the c n ’ s are constants called the coefficients of the series.

6. Find a power series for the following function. Show four terms and a general term. Also give the series using sigma notation and give the interval of convergence

9. Power Series By Substitution 5. Using the power series from example 2 make a new power series for

10. Power Series By Substitution 6. Using the power series from example 3 make a new power series for

11. Power Series By Differentiation 7.Use the power series for to write a power series for

12. Power Series By Differentiation 8.If Find 9. Identify the function j(x)

13. Power Series By Integration 10. Since then

14. Power Series By Substitution 11. Use the result of example 10 to write a power series for

15. Power Series By Substitution 12. Write a power series for

16. H OME W ORK Worksheet 9-3