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