## Calculus (3rd Edition)

$$1/2.$$
We have $$\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\cdots\\ =\frac{1}{4}(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\cdots) .$$ This is a gemetric series with the sum $$\frac{1/4}{1-(1/2)}=\frac{1}{4-2}=1/2.$$