# How do you find the sum of the infinite geometric series 27+9+3+1+...?

##### 3 Answers

Jul 11, 2018

#### Explanation:

The given infinite geometric series

has first term

Hence the sum of given infinite G.P.

Jul 11, 2018

#### Explanation:

#"the sum to infinity of a geometric series is"#

#â€¢color(white)(x)S_oo =a/(1-r)to -1 < r <1#

#"where a is the first term and r the common ratio"#

#"here "a=27" and "r=9/27=3/9=1/3#

#S_oo=27/(1-1/3)=27/(2/3)=81/2#

Jul 11, 2018

The answer is

#### Explanation:

If the common ratio of a geometric series is

Then,

The sum of the infinite geometric series

is given by .

Here the series is

and