Sum of Infinite Geometric Series

S=\frac{a_{1}}{1-r},\ if\ \lvert r \rvert <1

a_{1}=\ the\ first\ term\ in\ the\ series

r=\ common\ ratio

 

Example: Find the sum of the infinite geometric series. 9+3+1+…

S=\frac{a_{1}}{1-r}

a_{1}=9

r=\frac{3}{9}=\frac{1}{3}

S=\frac{9}{1-\frac{1}{3}}

S=\frac{9}{\frac{2}{3}}

S=13.5