Ta có :
\(2017A=\dfrac{2017\left(2017^{2015}+1\right)}{2017^{2016}+1}\)
\(=\dfrac{2017^{2016}+2017}{2017^{2016}+1}\)
\(=\dfrac{\left(2017^{2016}+1\right)+2016}{2017^{2016}+1}\)
\(=\dfrac{2017^{2016}+1}{2017^{2016}+1}\) + \(\dfrac{2016}{2017^{2016}+1}\)
\(=1+\dfrac{2016}{2017^{2016}+1}\) (1)
Tương tự :
\(2017B=\dfrac{2017\left(2017^{2014}+1\right)}{2017^{2015}+1}\)
\(=\dfrac{2017^{2015}+2017}{2017^{2015}+1}\)
\(=1+\dfrac{2016}{2017^{2016}+1}\) (2)
Từ (1) và (2) => \(2017A< 2017B\)
=> \(A< B\)
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