Câu hỏi của Lê Ánh Diễm My

Question

tính nhanh D = 2/3 + 2/6 + 2/12 +2/24 +.... + 2/768

Nguyễn Ngọc Anh Minh · Accepted Answer

$\dfrac{3}{2}xD=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}$

Đặt

$A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}$

$2xA=2+1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}$

$A=2xA-A=2-\dfrac{1}{256}=\dfrac{511}{256}=\dfrac{3}{2}xD$

$\Rightarrow D=\dfrac{511}{256}:\dfrac{3}{2}$Câu trả lời: $\dfrac{3}{2}xD=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}$

Đặt

$A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}$

$2xA=2+1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}$

$A=2xA-A=2-\dfrac{1}{256}=\dfrac{511}{256}=\dfrac{3}{2}xD$

$\Rightarrow D=\dfrac{511}{256}:\dfrac{3}{2}$