Đáp án: $A = \frac{{{2^{100}} - 1}}{{{2^{99}}}}$
Giải thích các bước giải:
$\begin{array}{l}
A = 1 + \frac{1}{2} + \frac{1}{{{2^2}}} + \frac{1}{{{2^3}}} + ... + \frac{1}{{{2^{99}}}}\\
\Rightarrow 2A = 2 + 1 + \frac{1}{2} + \frac{1}{{{2^2}}} + ... + \frac{1}{{{2^{98}}}}\\
\Rightarrow 2A - A = 2 - \frac{1}{{{2^{99}}}}\\
\Rightarrow A = 2 - \frac{1}{{{2^{99}}}} = \frac{{{2^{100}} - 1}}{{{2^{99}}}}
\end{array}$
