Đáp án: 127/128

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Giải thích các bước giả

Đáp án:

\( \frac{{127}}{{128}}\)

Giải thích các bước giải: $\begin{array}{l} A = \left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}} \right)\\ \Rightarrow 2.A = 2.\left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}} \right)\\ \,\,\,\,\,\,\,2.A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}}\\ \Rightarrow 2.A - A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} - \left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}} \right)\\ \Rightarrow A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} - \frac{1}{2} - \frac{1}{4} - \frac{1}{8} - \frac{1}{{16}} - \frac{1}{{32}} - \frac{1}{{64}} - \frac{1}{{128}}\\ \Rightarrow A = 1 - \frac{1}{{128}} = \frac{{127}}{{128}}. \end{array}$