How to write this fraction as sum of $2^{-n}$?

Question

I am trying to write the fraction $$\frac{29}{160}$$ as a sum of $2^{-n}$ such that $0\leq n\leq22$ but I can use each n only one time, wich means I cannot write the following $$\frac{1}{2^3}+\frac{1}{2^3}+...$$

Is it even possible to do that? what Is the actuall mathematic equation I should constract?

P.S

I dont have to use all the values for $n$

Answer 1

It is not be possible, because the number equals $\frac{29}{ 2^4 \cdot 10}$, and the binary expansion of $\frac{1}{ 10}$ doesn't terminate. (And $10$ is coprime with $29$)