Find the sum of the infinite geometric series 5 + 5/3 + 5/9 + 5/27 ..if it exists

1 Answer | Add Yours

lemjay's profile pic

lemjay | High School Teacher | (Level 2) Senior Educator

Posted on

Find the sum of the infinite geometric series 5 + 5/3 + 5/9 + 5/27 ..if it exists.

First, solve for the common ratio between consecutive terms.

`r=(5/3)/5=1/3`

`r=(5/9)/(5/3)=1/3`

`r=(5/27)/(5/9)=1/3`

Then, plug-in r=1/3 and a1=5 to the formula of sum of infinite geometric series.

`S_(oo)=a_1/(1-r)`

`S_(oo)=5/(1-1/3)=5/(2/3)=15/2`

Hence, the sum of the given infinite geometric series is `15/2` .

We’ve answered 315,880 questions. We can answer yours, too.

Ask a question