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Question

A=1/2+1/2²+1/2³+...+1/2¹³+1/2¹⁴

Tran Le Khanh Linh · Accepted Answer

$A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{13}}+\frac{1}{2^{14}}$

$\Leftrightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{13}}+\frac{1}{2^{14}}\right)$

$\Leftrightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}+\frac{1}{2^{13}}$

$\Leftrightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{12}}+\frac{1}{2^{13}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{13}}+\frac{1}{2^{14}}\right)$

$\Leftrightarrow A=1-\frac{1}{2^{14}}$

Câu trả lời:

$A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{13}}+\frac{1}{2^{14}}$

$\Leftrightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{13}}+\frac{1}{2^{14}}\right)$

$\Leftrightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}+\frac{1}{2^{13}}$

$\Leftrightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{12}}+\frac{1}{2^{13}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{13}}+\frac{1}{2^{14}}\right)$

$\Leftrightarrow A=1-\frac{1}{2^{14}}$

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