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Simplify s

Source: 1971 AHSME Problem 32

April 24, 2014
AMC

Problem Statement

If s=(1+2−132)(1+2−116)(1+2−18)(1+2−14)(1+2−12)s=(1+2^{-\frac{1}{32}})(1+2^{-\frac{1}{16}})(1+2^{-\frac{1}{8}})(1+2^{-\frac{1}{4}})(1+2^{-\frac{1}{2}}), then ss is equal to
<spanclass=′latex−bold′>(A)</span>12(1−2−132)−1<spanclass=′latex−bold′>(B)</span>(1−2−132)−1<spanclass=′latex−bold′>(C)</span>1−2−132<span class='latex-bold'>(A) </span>\textstyle{\frac{1}{2}}(1-2^{-\frac{1}{32}})^{-1}\qquad<span class='latex-bold'>(B) </span>(1-2^{-\frac{1}{32}})^{-1}\qquad<span class='latex-bold'>(C) </span>1-2^{-\frac{1}{32}}\qquad
<spanclass=′latex−bold′>(D)</span>12(1−2−132)<spanclass=′latex−bold′>(E)</span>12<span class='latex-bold'>(D) </span>\textstyle{\frac{1}{2}}(1-2^{-\frac{1}{32}})\qquad <span class='latex-bold'>(E) </span>\frac{1}{2}
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