Đáp án:
A = $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + ... + $\frac{1}{512}$ + $\frac{1}{1024}$
A = $\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + ... + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$
$\frac{1}{2}$ . A = $\frac{1}{2}$ . ($\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + ... + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$)
$\frac{1}{2}$ . A = $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + $\frac{1}{2^{4}}$ + ... + $\frac{1}{2^{10}}$ + $\frac{1}{2^{11}}$
A - $\frac{1}{2}$ . A = ($\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + ... + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$) - ($\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + $\frac{1}{2^{4}}$ + ... + $\frac{1}{2^{10}}$ + $\frac{1}{2^{11}}$)
$\frac{1}{2}$ . A = $\frac{1}{2^{1}}$ - $\frac{1}{2^{11}}$
A = ($\frac{1}{2}$ - $\frac{1}{2048}$) . 2
A = $\frac{1023}{1024}$.
Chúc học tốt!!!
