One Minus A Colorful Sum

Algebra Level 2

Simplify the colorful expression below. \[{1-\left(\dfrac{1}{\color{Blue}{2}}+\dfrac{1}{\color{Red}{4}}+\dfrac{1}{\color{Green}{8}}+\dfrac{1}{\color{Brown}{16}}+\dfrac{1}{\color{Magenta}{32}}+\dfrac{1}{\color{Orange}{64}}+\dfrac{1}{\color{Purple}{128}}+\dfrac{1}{\color{Gray}{256}}\right)}\]

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