Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

The sum of an infinite geometric series is:

r

aS

11

provided l r l < 1.

If l r l > 1, then the series has no sum.

r

aS

11

3

0 2

13 .1

n

n

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the sum of the infinite geometric series, if it has one.

2

1 3

0

1

a 3

2

1

213

6

r

aS

11

2

0 2

12 .2

n

n

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the sum of the infinite geometric series, if it has one.

2

1 2

0

1

a 2

2

1

3

4

232

r

aS

11

1

1

19.0 .3n

n

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the sum of the infinite geometric series, if it has one.

9.0 01 a 1 9.0

101.0

1

sum. no has series the,13

4 since

0 3

43 .4

n

n

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the sum of the infinite geometric series, if it has one.

r

aS

11

9 ,30 .5 1 aS

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the common ratio of the infinite series with the given sum and first term.

30 9

r3030 30

21r9

2130 r 10

7

r

aS

11

4 ,3 .6 1 aS

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the common ratio of the infinite series with the given sum and first term.

3 4

r33

3

1r

413 r

r

aS

11

1 ,2 .7 1 aS

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the common ratio of the infinite series with the given sum and first term.

2 1

r22

2

1r

112 r

r

aS

11

20 ,100 .8 1 aS

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Find the common ratio of the infinite series with the given sum and first term.

100 20

r100100 100

80r

2080100 r 5

4

32 1.11.11.1

r

aS

11

111.0 .9

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Write the repeating decimal as a fraction.

1.1.

9.

1.

9

1

32 1.31.31.3

r

aS

11

333.0 .10

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Write the repeating decimal as a fraction.

1.3.

9.

3.

9

3

3

1

201.7101.71

r

aS

11

7171.0 .11

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Write the repeating decimal as a fraction.

01.71.

99.

71.

99

71

201.2701.27

r

aS

11

2727.0 .12

Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences

Write the repeating decimal as a fraction.

01.27.

99.

27.

99

27

11

3

Notes Over 11.4