\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{16}+...-\dfrac{1}{128}\)
\(A=1-\dfrac{1}{128}=\dfrac{127}{128}\)
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