Infinite Geometric Series

Write in sigma notation

3 + 6 + 12 + 24 + 48

Write in sigma notation

-3 + 9 + -27 + 81 + -243

Write in sigma notation

-2 + 4 + -8 + 16 + -32 + 64

Infinite Geometric Series

In an infinite series, Sn approaches some limit as n becomes very large. That limit is defined to be the sum of the series. If an infinite series has a sum, it is said to converge.

A series converges (or has a sum) if and only if

Does the sum of each term approach some limit?

...64

1

32

1

16

1

8

1

4

1

2

1

Does the geom. series have a sum?

...81

1

27

1

9

1

3

11

Does the geom. series have a sum?

...625

3

125

3

25

3

5

33

Does the series have a sum?

To find the sum of an infinite series

Make sure a limit exists first

r

aSn

1

1

An infinite series in sigma notation—find the sum

1

1 5

124

n

n

An infinite series in sigma notation—find the sum

1

1 2

15

n

n

Writing a repeating decimal as a fraction

39.0

Writing a repeating decimal as a fraction

127.0