1. Splash Screen

2. Concept P. 683

3. Example 1A Convergent and Divergent Series A. Determine whether the infinite geometric series is convergent or divergent. 729 + 243 + 81 + … Find the value of r. Answer: Since the series is convergent.

4. Example 1B Convergent and Divergent Series B. Determine whether the infinite geometric series is convergent or divergent. 2 + 5 + 12.5 + … Answer: Since 2.5 > 1, the series is divergent.

5. Example 1A A.convergent B.divergent A. Determine whether the infinite geometric series is convergent or divergent. 343 + 49 + 7 + …

6. Example 1B A.convergent B.divergent B. Determine whether the infinite geometric series is convergent or divergent. 4 + 14 + 49 + …

7. Concept P. 684

8. Example 2A Sum of an Infinite Series Find the value of r to determine if the sum exists. Answer: The sum does not exist. A. Find the sum of, if it exists. the series diverges and the sum does not exist.

9. Example 2B Sum of an Infinite Series B. Find the sum of, if it exists. the sum exists. Now use the formula for the sum of an infinite geometric series. Sum formula

10. Example 2B Sum of an Infinite Series Simplify. Answer: The sum of the series is 2. a 1 = 3, r =

11. Example 2A A.4 B.1 C.2 D.no sum A. Find the sum of the infinite geometric series, if it exists. 2 + 4 + 8 + 16 +...

12. Example 2 A.4 B.2 C.1 D.no sum B. Find the sum of the infinite geometric series, if it exists.

13. Example 3 Infinite Series in Sigma Notation Sum formula Simplify. a 1 = 5, r = Evaluate. Answer: Thus,

14. Example 3 Evaluate. A.6 B.3 C. D.no sum

15. Example 4 Write a Repeating Decimal as a Fraction Use the sum of an infinite series. Write the repeating decimal as a sum. Write 0.25 as a fraction. Sum formula

16. Example 4 Write a Repeating Decimal as a Fraction Subtract. Simplify.

17. Example 4 Write 0.37 as a fraction. A. B. C. D.

18. Homework: p. 686 #3 – 39 (x3) skip #9

19. End of the Lesson