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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(\frac{2014}{2015}+\frac{2015}{2016}=1-\frac{1}{2015}+1-\frac{1}{2016}\)
\(=\left(1+1\right)-\left(\frac{1}{2015}+\frac{1}{2016}\right)=2-\left(\frac{1}{2015}+\frac{1}{2016}\right)< 2\)
Lại có :
\(\frac{2014}{2015}+\frac{2215}{2016}=1-\frac{1}{2015}+1+\frac{199}{2016}=2+\left(\frac{199}{2016}-\frac{1}{2015}\right)\)
\(=2+\frac{400985}{4062240}-\frac{2016}{4062240}=2+\frac{398969}{4062240}>2\)
\(\text{Vậy }\frac{2014}{2015}+\frac{2015}{2016}< \frac{2014}{2015}+\frac{2215}{2016}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2014\times2016=\left(2015-1\right)\times\left(2015+1\right)=2015\times2015-1
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tâ có :
B = 2014 x 2016 + 2015
B = 2014 x 2016 + 2016 - 1
B = 2016 x ( 2014 + 1 ) - 1
B = 2016 x 2015 - 1
Vậy A = B
![](https://rs.olm.vn/images/avt/0.png?1311)
\(4068288;4068289\)
VẬY \(2016\)NHÂN \(2018>\)\(2017\)NHÂN \(2017\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
A = 2014 x 2016 = 2014 x ( 2015 + 1 ) = 2014 + 2014 x 2015
B = 2015 x 2015 = ( 2014 + 1 ) x 2015 = 2014 x 2015 + 2015
Vì 2014 < 2015 => A < B
A = 2016 x 2016
B = 2018 x 2014
A = 2016 x ( 2014 + 2 )
A = 2016 x 2014 + 2016 x 2
B = 2018 x 2014
B = ( 2016 + 2 ) x 2014
B = 2016 x 2014 + 2 x 2014
Vì 2016 x 2014 = 2016 x 2014, mà 2016 x 2 > 2 x 2014
=> A > B
A = 2016 x 2016
A = (2018 - 2) x (2014 + 2)
A = 2018 x (2014 + 2 ) - 2 x (2014 + 2)
A = 2018 x 2014 + 4036 - 4028 + 4
A = 2018 x 2014 + 12
Mà B = 2018 x 2014
=> A > B