![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+...+\frac{1}{1280}\)
\(=\left(\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+...+\frac{1}{1280}\right)\cdot5\cdot\frac{1}{5}\)
\(=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...-\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\left(1+1-\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\left(2-\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\frac{511}{256}\cdot\frac{1}{5}\)
\(=\frac{511}{1280}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt biểu thức trên là A
\(5A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)
Đặt \(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+..+\frac{1}{128}\)
\(2B=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)
\(B=2B-B=1-\frac{1}{128}=\frac{127}{128}\)
\(5A=1+\frac{127}{128}=\frac{255}{128}\Rightarrow A=\frac{5A}{5}=\frac{51}{128}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2,4+4+2}{8,4}=8,4:8,4=1\)