1. Warming Up

2. 13.5: Sums of Infinite Series Pre-Calculus

3. Objectives : 1. Evaluate Infinite Series 2. Find interval of convergence 3. Evaluate repeating decimals Vocabulary : converge, diverge, interval of convergence 13.5 Sum of Infinite Series

4. Learning the Lingo/ Rules

5. Example: Find the sum of the infinite geometric series: 9 – 6 + 4 – …

6. Quick Practice! Find the sum of the given infinite series, otherwise state that it diverges! 10/9

7. Explain why the series converges or diverges. Show mathematical proof. 1 + 3 + 9 + 27 + …

8. Solution (1 < x < 3) is called the “interval of convergence”

9. For what values of x does the following infinite series converge? -1 < x < 1

10. The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. What is the total vertical distance that the ball will travel before it stops? 50 40 32 128/5 40 32 128/5

11. An old grandfather clock is broken. When the pendulum is swung it follows a swing pattern of 25 cm, 20 cm, 16 cm, and so on until it comes to rest. What is the total distance the pendulum swings before coming to rest? 25 20 16 25 20 16

12. The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. What is the total vertical distance that the ball will travel before it stops? 100 75 225/4 100 75 225/4

13. Practice TB P.502: 1-17 odd, 33, 34, 39, 40