# What is the sum of the infinite geometric series sum_(n=1)^oo(1/3)^n ?

This is a geometric series with first term $\frac{1}{3}$ and common ratio $\frac{1}{3}$ (see geometric series ).
The common ratio is less than 1 in absolute value, so that the series is convergent and its sum is given by "first term"/(1-"common ratio")=(1/3)/(1-(1/3))=1/2