1. Copyright © 2011 Pearson, Inc. 9.5 Series Goals: Use sigma notation to find the finite sums of terms in arithmetic and geometric sequences. Find sums of convergent geometric series.

2. Copyright © 2011 Pearson, Inc. Slide 9.5 - 2 What you’ll learn about Summation Notation Sums of Arithmetic and Geometric Sequences Infinite Series Convergence of Geometric Series … and why Infinite series are at the heart of integral calculus.

3. Copyright © 2011 Pearson, Inc. Slide 9.5 - 3 Summation Notation

4. Copyright © 2011 Pearson, Inc. Slide 9.5 - 4 Infinite Series

5. Copyright © 2011 Pearson, Inc. Example: Sigma Notation Slide 9.5 - 5

6. Copyright © 2011 Pearson, Inc. How Many Terms? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 43, 44, 45, 46, …, 93 2, 4, 6, 8, 10, …, 18 2, 5, 8, 11, …, 29 Slide 9.5 - 6

7. Copyright © 2011 Pearson, Inc. Example: Write Using Summation Notation Slide 9.5 - 7

8. Copyright © 2011 Pearson, Inc. Karl Friedrich Gauss (1777-1855) Slide 9.5 - 8

9. Copyright © 2011 Pearson, Inc. Slide 9.5 - 9 Sum of a Finite Arithmetic Sequence

10. Copyright © 2011 Pearson, Inc. Slide 9.5 - 10 Example: Summing the Terms of an Arithmetic Sequence

11. Copyright © 2011 Pearson, Inc. Slide 9.5 - 11 Example: Summing the Terms of an Arithmetic Sequence

12. Copyright © 2011 Pearson, Inc. Slide 9.5 - 12 Sum of a Finite Geometric Sequence

13. Copyright © 2011 Pearson, Inc. Slide 9.5 - 13 Sum of an Infinite Geometric Series

14. Copyright © 2011 Pearson, Inc. Example: Summing Finite Geometric Series Slide 9.5 - 14

15. Copyright © 2011 Pearson, Inc. Example: Summing Finite Geometric Series Slide 9.5 - 15

16. Copyright © 2011 Pearson, Inc. Example: Summing Finite Series Slide 9.5 - 16

17. Copyright © 2011 Pearson, Inc. Slide 9.5 - 17 Example: Summing Infinite Geometric Series

18. Copyright © 2011 Pearson, Inc. Example: Summing Infinite Geometric Series Determine whether each series converges. If it converges, give the sum. Slide 9.5 - 18