Question

So sánh :

A = \(\dfrac{2017^{2015}+1}{2017^{2016}+1}\)

B = \(\dfrac{2017^{2014}+1}{2017^{2015}+1}\)

Answer 1

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) => \(2017A< 2017B\)

=> \(A< B\)