Bài giải:

$\begin{align}& \left( x+\frac{1}{2} \right)+\left( x+\frac{1}{4} \right)+\left( x+\frac{1}{8} \right)+\left( x+\frac{1}{16} \right)=1 \\ & 4\times x+\left( \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16} \right)=1 \\ & 4\times x+\frac{15}{16}=1 \\ & 4\times x=1-\frac{15}{16} \\ & 4\times x=\frac{1}{16} \\ & x=\frac{1}{16}:4 \\  & x=\frac{1}{64} \\ \end{align}$