EXAMPLE 1 Find partial sums SOLUTION S 1 = 1 2 = 0.5 S 2 = = S 3 = 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

EXAMPLE 1 Find partial sums From the graph, S n appears to approach 1 as n increases. S4=S4= S 5 =

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 – = 25 S = a1a1 1 – r = 1 ( ) 1 – 3 4 = b. + – – b. For this series, a 1 = 1 and r = –. 3 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.

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

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

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