1. Series and Convergence Lesson 9.2

2. Definition of Series Consider summing the terms of an infinite sequence We often look at a partial sum of n terms

3. Definition of Series We can also look at a sequence of partial sums { S n } The series can converge with sum S The sequence of partial sums converges If the sequence { S n } does not converge, the series diverges and has no sum

4. Examples Convergent Divergent

5. Telescoping Series Consider the series Note how these could be regrouped and the end result As n gets large, the series = 1

6. Geometric Series Definition An infinite series The ratio of successive terms in the series is a constant Example What is r ?

7. Properties of Infinite Series Linearity The series of a sum = the sum of the series Use the property

8. Geometric Series Theorem Given geometric series (with a ≠ 0) Series will Diverge when | r | ≥ 1 Converge when | r | < 1 Examples Compound interest Or

9. Applications A pendulum is released through an arc of length 20 cm from vertical Allowed to swing freely until stop, each swing 90% as far as preceding How far will it travel until it comes to rest? 20 cm

10. Assignment Lesson 9.2 Page 612 Exercises 1 – 69 EOO