Câu hỏi của Itachi

Question

A=1/2+1/2mu2+1/2mu3+.....+1/2mu10

Chứng minh: A+1/2mu10=1

Đinh Tuấn Việt · Accepted Answer

$\Rightarrow\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{11}}$

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

Vậy $A=\left(\frac{1}{2^{10}}-\frac{1}{2}\right):\frac{1}{2}=\frac{2}{2^{10}}-1$

Do đó $A+\frac{1}{2^{10}}=\frac{2}{2^{10}}-1+\frac{2}{10}=1$

Câu trả lời:

$\Rightarrow\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{11}}$

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

Vậy $A=\left(\frac{1}{2^{10}}-\frac{1}{2}\right):\frac{1}{2}=\frac{2}{2^{10}}-1$

Do đó $A+\frac{1}{2^{10}}=\frac{2}{2^{10}}-1+\frac{2}{10}=1$