1. WARM UP

2. 12.4 Infinite Geometric Series EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum.

3. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Key Term Partial Sum – The sum S n of the first n terms of an infinite series. Partial Sum – The sum S n of the first n terms of an infinite series.

4. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 1 Find partial sums

5. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 1 Find partial sums

6. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum.

7. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 2 Find sums of infinite geometric series Find the sum of the infinite geometric series. a. 5(0.8) i – 1 8 i = 1 3 4 9 16 27 64 b. + – +... 1 –

8. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 2 Find sums of infinite geometric series Find the sum of the infinite geometric series, if it exists. + 3 4 + + d. 3 3 16 3 64... + c. 8 n = 1 n – 1 5 4 3

9. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 3 Standardized Test Practice

10. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 4 Application Pendulums A pendulum that is released to swing freely travels 18 inches on the first swing. On each successive swing, the pendulum travels 80% of the distance of the previous swing. What is the total distance the pendulum swings?

11. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 5 Write repeating decimals as fractions a. Write 0.242424... as a fraction in lowest terms.a. Write 0.242424... as a fraction in lowest terms.

12. EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 5 Write repeating decimals as fractions Write the repeating decimal as a fraction in lowest terms. b. 0.555...

13. Homework Textbook Pg. 823-824 3-27(3) and 37