EXAMPLE 1 Find partial sums

SOLUTION

S1 =12 = 0.5

S2 =12

14+ = 0.75

18S3 =

12

14+ + 0.88

. . . . Find and graph the partial sums Sn for n = 1, 2, 3, 4, and 5. Then describe what happens to Sn as n increases.

Consider the infinite geometric series 12

14

18

+ + 116+

1

32+ +

EXAMPLE 1 Find partial sums

From the graph, Sn appears to approach 1 as n increases.

S4=12

14+

18+ 1

16+ 0.94

S5 =12

14+

18+ 1

16+ 132+ 0.97

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, a1 = 5 and r = 0.8.

S =a1

1 – r = 1 – 0.85

= 25

S =a1

1 – r =1

( )1 – 34

= 47

34

916

2764

b. + – +. . .1 –

b. For this series, a1 = 1 and r = – . 34

EXAMPLE 3 Standardized Test Practice

SOLUTION

Because – 3 ≥ 1 the sum does not exist.

ANSWER

The correct answer is D.

You know that a1 = 1 and a2 = – 3. So, r – 31 = – 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 Sn for n = 1, 2, 3, 4 and 5. Then describe what happens to Sn as n increases.

25

425 125

862516

312532

GUIDED PRACTICE for Examples 1, 2 and 3

S1 =

S2 0.56

S3 0.62

S4 0.66

Sn appears to be approaching

as n increases.

ANSWER

23

25

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

12

–

23ANSWER

3.

8

n = 1

n – 1543

no sumANSWER

+ 34 + +4. 3 3

163

64. . .+

4ANSWER