So sánh a và b biết a=2015^2016-2015^2015 ,b=2015^2017-2015^2016
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2015^{2016}-2015^{2015}\)
\(=2015^{2015}\left(2015-1\right)\)
\(=2015^{2015}.2014\)
\(B=2015^{2017}-2015^{2016}\)
\(=2015^{2016}\left(2015-1\right)\)
\(=2015^{2016}.2014\)
Vì \(2015^{2015}< 2015^{2016}\)
nên \(A< B\)
Ta có :
\(2015^{2016}< 2015^{2017}\)
\(2015^{2015}< 2015^{2016}\)
\(\Rightarrow\)\(A=2015^{2016}-2015^{2015}< B=2015^{2017}-2015^{2016}\)
Vậy \(A< B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(A=2015^{2016}-2015^{2015}=2015^{2015}\left(2015-1\right)=2015^{2015}.2014\)
\(B=2015^{2017}-2015^{2016}=2015^{2016}\left(2015-1\right)=2015^{2016}.2014\)
Vì \(2015^{2015}< 2015^{2016}\) nên \(2015^{2015}.2014< 2015^{2016}.2014\) hay \(A< B\)
Vậy \(A< B\)
Chúc bạn học tốt ~
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt 2015.2016+2016=n
suy ra A=(n+1)/n và B=(n+2)/(n+1)
Ta có A - B=(n+1)/n -(n+2)/(n+1)=((n+1)2-n(n+2))/n(n+1)=(n2+2n+1-n2-2n)/n(n+1)=1/n(n+1)
Vì A-B lớn hơn 0 nên A>B
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{2015}{2016}+\frac{2016}{2017}=1-\frac{1}{2016}+1-\frac{1}{2017}>1\)
\(B=\frac{2015+2016}{2016+2017}< \frac{2016+2017}{2016+2017}=1\)
Suy ra \(A>B\).
![](https://rs.olm.vn/images/avt/0.png?1311)
- \(A=\frac{2015}{2016}+\frac{2016}{2017}>1;\)
- \(B=\frac{2015+2016}{2016+2017}< 1\)
- Nên A>B
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
1 - A = 1 - 2014/2015 = 1/2015
1 - B = 1 - 2015/ 2016 = 1/2016
Vì 1/2015 > 1/2016 => 1 - 2014/2015 > 1 - 2015 / 2016
Hay 1 - A > 1 -B => A < B
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2015}{2016}+\frac{2016}{2017}>\frac{\left(2015+2016\right)}{\left(2016+2017\right)}=\frac{2015}{2016+2017}+\frac{2016}{2016+2017}\)
![](https://rs.olm.vn/images/avt/0.png?1311)