# How do you find the sum of the infinite geometric series given #5/3-10/9+20/27-...#?

##### 3 Answers

#### Explanation:

We first find the factor :

The sum of an infinite geometric series is given by the formula :

So the sum is :

Sum of the infinite geometric series is

#### Explanation:

In the series

whilr first term

As for common ratio

sum of the infinite geometric series is

#### Explanation:

#"for a geometric sequence the sum of n terms is"#

#S_n=(a(1-r^n))/(1-r);(r!=1)#

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

#"as " ntooo,r^nto0" and " S_n" can be expressed as"#

#S_oo=a/(1-r);(|r|<1)#

#rArrr=(-10/9)/(5/3)=-2/3rarr|r|<1#

#rArrS_oo=(5/3)/(1+2/3)=1#