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Ta có : \(\frac{1}{5}< 1;\frac{97}{96}>\frac{96}{96}=1;\frac{2000}{2000}=1;\frac{562}{1}=562>1\)
Khi đó ta so sánh : \(\frac{1}{5}< \frac{2000}{2000}< \frac{97}{96}< \frac{562}{1}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(A=\frac{3}{4.5}+\frac{3}{5.6}+\frac{3}{6.7}+...+\frac{3}{99.100}\)
\(A=3\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{99.100}\right)\)
\(A=3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=3\left(\frac{1}{4}-\frac{1}{100}\right)\)
\(A=3.\frac{6}{25}\)
\(A=\frac{18}{25}\)
Vậy \(A=\frac{18}{25}\)
Chúc bạn học tốt ~
\(A=\frac{3}{4.5}+\frac{3}{5.6}+\frac{3}{6.7}+...+\frac{3}{99.100}\)
\(\Rightarrow A=3.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{99.100}\right)\)
\(\Rightarrow A=3.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(\Rightarrow A=3.\left(\frac{1}{4}-\frac{1}{100}\right)=\frac{3.24}{100}\)
\(=\frac{3.4.6}{25.4}\)
\(\Rightarrow A=\frac{18}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
sua lai :
1015/1016<1016/1015
nen :1+1015/1016<1+1016/1015
![](https://rs.olm.vn/images/avt/0.png?1311)
1/5 ; 2000/2000 ; 97/96 ; 562/1