1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 9.5 Testing Convergence at Endpoints

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 3 Quick Review

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 4 Quick Review Solutions

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 5 Quick Review Solutions

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 6 What you’ll learn about Integral Test Harmonic Series and p-series Comparison Tests Alternating Series Absolute and Conditional Convergence Intervals of Convergence A Word of Caution … and why Additional tests for convergence of series are introduced in this section.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 7 The Integral Test

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 8 Example Applying the Integral Test

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 9 Harmonic Series p-series

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 10 The Limit Comparison Test (LCT)

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 11 Example Using the Limit Comparison Test

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 12 The Alternating Series Test (Leibniz’s Theorem)

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 13 The Alternating Series Estimation Theorem

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 14 Rearrangement of Absolutely Convergent Series

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 15 Rearrangement of Conditionally Convergent Series

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 16 How to Test a Power Series for Convergence

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 17 Example Finding Intervals of Convergence

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 18 Procedure for Determining Convergence

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 19 Quick Quiz Sections 9.4 and 9.5

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 20 Quick Quiz Sections 9.4 and 9.5

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 21 Quick Quiz Sections 9.4 and 9.5

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 22 Quick Quiz Sections 9.4 and 9.5

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 23 Quick Quiz Sections 9.4 and 9.5

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 24 Quick Quiz Sections 9.4 and 9.5

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 25 Chapter Test

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 26 Chapter Test

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 27 Chapter Test

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 28 Chapter Test

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 29 Chapter Test Solutions

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 30 Chapter Test Solutions

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 31 Chapter Test Solutions

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 32 Chapter Test Solutions