so sánh \(\frac{20132013}{20152015}\)và \(\frac{20152015}{20172017}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
( 20152015/20162016 + 20172017/20162016 ) . x - 1 = 2016
2.x-1=2016
2x=2017
x=2017:2
x=1008,5
![](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)
\(\frac{20152015}{20162016}+\frac{20162016}{20162016}\)
\(=\frac{2015\times10001}{2016\times10001}+\frac{2016\times10001}{2016\times10001}\)
\(=\frac{2015}{2016}+\frac{2016}{2016}\)
\(=\frac{4031}{2016}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta thấy:
A = \(\frac{20162017}{20162016}\) và B = \(\frac{20152016}{20152015}\)
A = \(\frac{20162016}{20162016}\)+ \(\frac{1}{20162016}\) = \(1\) + \(\frac{1}{20162016}\)
B = \(\frac{20152015}{20152015}\) + \(\frac{1}{20152015}\)= \(1\) + \(\frac{1}{20152015}\)
Vì: \(\frac{1}{20162016}\) \(< \) \(\frac{1}{20152015}\)
Nên: \(A\) \(< \) \(B\)
~ HokT~
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2015}{2014}+\frac{-20152015}{20142014}-\frac{201520152015}{-201420142014}\)=\(\frac{2015}{2014}+\frac{-2015}{2014}-\frac{-2015}{2014}\)
=\(\frac{2015}{2014}+0=\frac{2015}{2014}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=20162016/20162016 + 1/20162016=1 + 1/20162016
B=20152015/20152015 + 1/20152015=1+1/20152015
Mà 20162016>20152015-->1/20162016<1/20152015 và 1=1
=>A<B
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{20132013}{20152015}=\frac{20132013:10001}{20152015:10001}=\frac{2013}{2015}=1-\frac{2}{2015}\)
\(\frac{20152015}{20172017}=\frac{20152015:10001}{20172017:10001}=\frac{2015}{2017}=1-\frac{1}{2017}\)
\(1-\frac{1}{2015}
ta có : \(\frac{20152015}{20172017}=\frac{2015}{2017}\)
\(\frac{20132013}{20152015}=1-\frac{20132013}{20152015}=\frac{2}{20152015}\)
\(\frac{2015}{2017}=1-\frac{2015}{2017}=\frac{2}{2017}\)
mà \(\frac{2}{2017}>\frac{2}{20152015}\) nên \(\frac{20152015}{20172017}