So sánh \(A=\frac{2017^{2016}+1}{2017^{2017}+1}\)và\(B=\frac{2017^{2017}+1}{2017^{2018}+1}\)
ta có: \(\left(2017^{2016}+1\right)\left(2017^{2018}+1\right)=2017^{2016+2018}+2017^{2016}+2017^{2018}+1\)
=\(2017^{4034}+2017^{2017}\cdot\frac{1}{2017}+2017^{2017}\cdot2017+1=2017^{4034}+2017^{2017}\left(\frac{1}{2017}+2017\right)+1\)
\(\left(2017^{2017}+1\right)\left(2017^{2017}+1\right)=2017^{4034}+2\cdot2017^{2017}+1\)
Vì \(2017+\frac{1}{2017}>2\)nên\(2017^{4034}+2017^{2017}\left(2017+\frac{1}{2017}\right)+1>2017^{4034}+2\cdot2017^{2017}+1\)
\(\Rightarrow\left(2017^{2016}+1\right)\left(2017^{2018}+1\right)>\left(2017^{2017}+1\right)\left(2017^{2017}+1\right)\)
\(\Rightarrow\frac{2017^{2016}+1}{2017^{2017}+1}>\frac{2017^{2017}+1}{2017^{2018}+1}\)
\(\Rightarrow A>B\)
