Sum of a geometric series $\sum_0^\infty \frac{1}{2^{1+2n}}$ $$\sum_0^\infty \frac{1}{2^{1+3n}}$$
So maybe I have written the sequence incorrectly, but how do I apply the $\frac{1}{1 - r}$ formula for summing a geometric sequence to this? When I do it I get something over one which is wrong because this is suppose to model a percentage of something.

This is
$$
\begin{align}
\frac12\sum_{n=0}^\infty\frac1{4^n}
&=\frac12\frac1{1-\frac14}\\
\end{align}
$$
