1. EXAMPLE 1 Find partial sums SOLUTION S 1 = 1 2 = 0.5 S 2 = 1 2 1 4 += 0.75 1 8 S 3 = 1 2 1 4 + + 0.88.... Find and graph the partial sums S n for n = 1, 2, 3, 4, and 5. Then describe what happens to S n as n increases. Consider the infinite geometric series 1 2 1 4 1 8 ++ 1 16 + 1 32 + +

2. EXAMPLE 1 Find partial sums From the graph, S n appears to approach 1 as n increases. S4=S4= 1 2 1 4 + 1 8 + 1 16 + 0.94 S 5 = 1 2 1 4 + 1 8 + 1 16 + 1 32 + 0.97

3. 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 SOLUTION a. For this series, a 1 = 5 and r = 0.8. S = a1a1 1 – r = 1 – 0.8 5 = 25 S = a1a1 1 – r = 1 ( ) 1 – 3 4 = 4 7 3 4 9 16 27 64 b. + – +... 1 – b. For this series, a 1 = 1 and r = –. 3 4

4. EXAMPLE 3 Standardized Test Practice SOLUTION Because – 3 ≥ 1 the sum does not exist. ANSWER The correct answer is D. You know that a 1 = 1 and a 2 = – 3. So, r – 3 1 = – 3.

5. GUIDED PRACTICE for Examples 1, 2 and 3 Find the sums of the infinite geometric series. 1.Consider the series + + + + +.... Find and graph the partial sums S n for n = 1, 2, 3, 4 and 5. Then describe what happens to S n as n increases. 2 5 4 25 125 8 625 16 3125 32

6. GUIDED PRACTICE for Examples 1, 2 and 3 S 1 = S 2  0.56 S 3  0.62 S 4  0.66 S n appears to be approaching as n increases. ANSWER 2 3 2 5

7. GUIDED PRACTICE for Examples 1, 2 and 3 Find the sum of the infinite geometric series, if it exists. 2. n – 1 8 n = 1 1 2 – 2 3 ANSWER 3. 8 n = 1 n – 1 5 4 3 no sum ANSWER + 3 4 + + 4. 3 3 16 3 64... + 4 ANSWER