p.675

11.4 Infinite Geometric Series11.4 Infinite Geometric Series

What is the formula for find the sum of an infinite geometric series?

Does an infinite geometric series have a sum if the

How do you write a repeating decimal as a fraction?

?1r

The sum of an The sum of an infinite geometric infinite geometric

seriesseries

1r if , 1

1

r

aS

sum. no is there,1 If r

1r if , 1

1

r

aS

ExampleExample: Find the sum of the : Find the sum of the infinite geometric series.infinite geometric series.

1

1)1.0(2i

i

For this series, aFor this series, a11=2 & r=0.1=2 & r=0.1

1.1

2

S

9

20

9.

2

ExampleExample: Find the sum of the : Find the sum of the series:series: ...

9

4

3

4412 So, a1=12

and r=1/3

31

1

12

S

32

12S

2

36S

S=18

Example: An infinite geom. Series has aExample: An infinite geom. Series has a11=4 & =4 &

a sum of 10. What is the common ratio?a sum of 10. What is the common ratio?

r

aSuse

1 1

r

1

410

10(1-r)=4

1-r = 2/5

-r = -3/5

5

3r

Example: Write 0.181818… as a Example: Write 0.181818… as a fraction.fraction.

0.181818…=18(.01)+18(.01)0.181818…=18(.01)+18(.01)22+18(.01)+18(.01)33+…+…

Now use the rule for the sum!Now use the rule for the sum!

r

a

11

01.1

18.

99.

18.

11

2

What is the formula for find the sum of an infinite geometric series?

Does an infinite geometric series have a sum if the

No!How do you write a repeating decimal as a fraction?Use the rule for sum and substitute in for

a1 and r.

?1r

1r if , 1

1

r

aS

r

aS

1 1

Assignment:Assignment:

p. 678p. 678

13-4313-43

oddodd