# How do you find the sum of the infinite geometric series Sigma (1/2)^n from n=0 to oo?

Realize that the sum of a geometric series of the form $\sum a {r}^{n}$ can be represented by $\frac{a}{1 - r}$ where $a$ is the first term of the series and $r$ is the common ratio. Thus we can see that the series $\sum {\left(\frac{1}{2}\right)}^{n}$ is of the form of a geometric series, where the r is 0.5 and the a is 1.
So the sum of our series becomes $\frac{1}{1 - \left(\frac{1}{2}\right)}$ which is $\frac{1}{0.5} = 2$