12.4 – Find Sums of Infinite Geometric Series

Think about this…

1

n

What will happen when n becomes really big?

It will get closer and closer to zero.

The Sum of an Infinite Geometric Series:

1

1na

Sr

ONLY IF: 1r

IF: 1r there is no sum

1. Find the sum of the geometric series.

1

1

455

i

i

1

1na

Sr

a1 = 5 r = < 14

5

54

15

5

1/ 5 5 5 25

2. Find the sum of the geometric series.

0

1

2

i

i

1

1na

Sr

a1 = 1 r = < 11

2

11

12

1

3 / 2

213

2

3

3. Find the sum of the geometric series.

1

0

1 5

2 4

i

i

a1 = 1/2 r = > 1

5

4

No Sum

4. Find the sum of the geometric series.

3 9 271 ...4 16 64

1

1na

Sr

a1 = 1 r = < 13

4

13

14

1

7 / 4

417

4

7

5. Find the sum of the geometric series.

4 83 2 ...

3 9

1

1na

Sr

a1 = 3 r = < 12

3

32

13

3

1/ 3

331

9

5. Find the sum of the geometric series.

36 2165 6 ...

5 25

a1 = 5 r = > 16

5

No Sum

6. Determine if the series is arithmetic, geometric, or infinite geometric.

1

0

124

i

i

infinite geometric

19

1

3 5i

i

i

arithmetic

4

0

152

i

i

geometric