Câu hỏi của Nguyễn Phương Linh

Question

tìm A biết A = 1/2+1/2^2+1/2^3+...+1/2^9

Ngoc Han ♪ · Accepted Answer

Ta có :

$\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}$

$\Rightarrow A-\frac{1}{2}A=\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)$

$\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{2^{10}}$

$\Rightarrow A=1-\frac{1}{2^9}=\frac{511}{512}$

Câu trả lời:

Ta có :

$\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}$

$\Rightarrow A-\frac{1}{2}A=\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)$

$\Rightarrow\frac{1}{2}A=\frac{1}{2}-\frac{1}{2^{10}}$

$\Rightarrow A=1-\frac{1}{2^9}=\frac{511}{512}$