Question

so sánh: 

a) A=\(\frac{2015^{2016}+1}{2015^{2017}+1}\)và B=\(\frac{2015^{2015}+1}{2015^{2016}+1}\)

Answer 1

Vì \(2015^{2016}+1< 2015^{2017}+1\Rightarrow\frac{2015^{2016}+1}{2015^{2017}+1}< 1\)

\(\Rightarrow A=\frac{2015^{2016}+1}{2015^{2017}+1}< \frac{2015^{2016}+1+2014}{2015^{2017}+1+2014}=\frac{2015\left(2015^{2015}+1\right)}{2015\left(2015^{2016}+1\right)}=\frac{2015^{2015}+1}{2015^{2016}+1}=B\)

Vậy \(A< B\)

Answer 2

\(2015A=\frac{2015^{2017}+2015}{2015^{2017}+1}=\frac{2015^{2017}+1+2014}{2015^{2017}+1}=1+\frac{2014}{2015^{2017}+1}\)

\(2015B=\frac{2015^{2016}+2015}{2015^{2016}+1}=\frac{2015^{2016}+1+2014}{2015^{2016}+1}=1+\frac{2014}{2015^{2016}+1}\)

vì \(\frac{2014}{2015^{2017}+1}< \frac{2014}{2015^{2016}+1}\)

nên \(2015A< 2015B\)

=> \(B>A\)

Answer 3

Ta có: 2015^2016+1<2015^2017 +1

=> 2015^2016 +1/ 2015^2017+1 <1

=> A= 2015^2016 +1/ 2015^2017+1 < 2015^2016+1+2014/2015^2017+1+2014=2015^2015+1/2015^2016+1=B

Vậy A<B

---k mk bn nhé--- Lâu rồi mới lên :*