Main Ideas/Questions Notes/Examples

Geometric Series

A geometric series is the _________ of a geometric sequence. To find the sum, use the following formula:

where n is the __________________________________________, a1 is the ________________________, and r is the ________________________________.

ExamplesDirections: Find the indicated sum for each geometric series. 1. { }

144 20 100 500 ... ; S+ + + + 2. { }2081 27 9 3 ... ; S+ + + +

3. { }3 6 12 24 ... 6144+ + + + + 4. { }4 12 36 108 ... 2916− + − + +

5. ( )25

1

12 n

n

−

=∑ 6.

18

1

1322

x

x

−

=

− ⋅ − ∑

7. 20

1

64 ( 3)k

k

−

=

− ⋅ −∑ 8. 111

2

1812

m

m

−

=

⋅ ∑

Name: ____________________________________________________

Class: ________________________________

Date: ________________________________

Topic: ____________________________________________________

© Gina Wilson (All Things Algebra), 201ϲ

AFM Name: Unit 5 Day 4 Notes: Geometric Series Date:

Infinite Geometric

Series

Find the partial sums for each infinite series below:

A series that approaches a certain sum is called a CONVERGENT SERIES.

A series that does not have a certain sum is called a DIVERGENT SERIES.

• If _____________, then the series is ______________________.

• If _____________, then the series is ______________________.

Convergent Series Formula

To find the sum of a convergent infinite geometric

series, use the formula:

Examples Determine if the series is converent or divergent. If convergent, find the sum.

9. 1 1 11 ...4 16 64

+ + + +

10. 2 8 32 128 ...3 3 3 3 + + + +

11.{ }5.8 3.48 2.088 1.2528 ...+ + + + 12. { }128 96 72 54 ...− + − +

13. 1

1

124

x

x

−∞

=

− ⋅

∑ 14. ( ) 1

17 0.8 p

p

∞−

=

⋅∑

15.1

4

582

w

w

−∞

=

⋅ − ∑ 16.

1

2

364

k

k

−∞

=

− ⋅ − ∑

1 1 1 1 ...2 4 8 16

+ + + +

1S

2S

3S

4S

5S S

{ }1 1 2 4 8 ...2+ + + + +

1S

2S

3S

4S

5S

6S

© Gina Wilson (All Things Algebra), 201ϲ