smc

Multiply both sides of the given equation by $(1-2^{-\frac{1}{32}})$. Using difference of squares reveals that $(1-2^{-\frac{1}{32}})(1+2^{-\frac{1}{32}})=(1-2^{-\frac{1}{16}})$. Thus, we can use difference of squares again on the next term, $(1+2^{-\frac{1}{16}})$, and the terms after that until we get $(1+2^{-\frac{1}{32}})s=(1-2^{-\frac{1}{2}})(1+2^{-\frac{1}{2}})=1-2^{-1}=\frac{1}{2}$. Dividing both sides by $(1+2^{-\frac{1}{32}})$ reveals that $s=\boxed{\frac{1}{2}(1-2^{-\frac{1}{32}}{)}^{-1}}$.