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

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### 1 Answer

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` .**