Tính nhanh tổng A=1/2+1/4+1/8+1/16+1/32+1/64+1/128

Tính nhanh tổng A=1/2+1/4+1/8+1/16+1/32+1/64+1/128

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  1. Đáp án:

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

    Giải thích các bước giải:

    $\begin{array}{l}
    A = \left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}} \right)\\
    \Rightarrow 2.A = 2.\left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}} \right)\\
    \,\,\,\,\,\,\,2.A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}}\\
    \Rightarrow 2.A – A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} – \left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} + \frac{1}{{128}}} \right)\\
    \Rightarrow A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}} – \frac{1}{2} – \frac{1}{4} – \frac{1}{8} – \frac{1}{{16}} – \frac{1}{{32}} – \frac{1}{{64}} – \frac{1}{{128}}\\
    \Rightarrow A = 1 – \frac{1}{{128}} = \frac{{127}}{{128}}.
    \end{array}$

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