1. 11.4 – Infinite Geometric Series

2. Sum of an Infinite Geometric Series

3. The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r

4. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible.

5. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + …

6. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r =

7. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ ½

8. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾ ½

9. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r

10. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r = ½ 1 – ¾

11. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r = ½ = ½ 1 – ¾ ¼

12. Sum of an Infinite Geometric Series The sum S of an infinite geometric series with -1<r<1 is given by S = a 1 1 – r Ex. 1 Find the sum of each infinite geometric series, if possible. a) ½ + ⅜ + … r = ⅜ = ¾, S = a 1 ½ 1 – r = ½ = ½ = 2 1 – ¾ ¼

13. b) 1 – 2 + 4 – 8 + …

14. r =

15. b) 1 – 2 + 4 – 8 + … r = -2 1

16. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1

17. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible.

18. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1

19. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1

20. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20

21. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼

22. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 1 – r

23. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 = 20 1 – r 1 – (- ¼)

24. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 = 20 = 20 1 – r 1 – (- ¼) 5 / 4

25. b) 1 – 2 + 4 – 8 + … r = -2 = -2 1 Since r is not -1<r<1, finding the sum of the series is not possible. ∞ Ex. 2 Evaluate ∑ 20(-¼) n – 1 n=1 a n = a 1 r n – 1 a 1 = 20 r = -¼ S = a 1 = 20 = 20 = 16 1 – r 1 – (- ¼) 5 / 4

26. Ex. 3 Write the following repeating decimals as fractions.

27. __ a) 0.39

28. Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 99

29. Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33

30. Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33 ___ b) 0.246

31. Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33 ___ b) 0.246 = 246 999

32. Ex. 3 Write the following repeating decimals as fractions. __ a) 0.39 = 39 = 13 99 33 ___ b) 0.246 = 246 = 82 999 333