Question

so sánh x và y biết : \(x=\dfrac{2016^{2017}+1}{2016^{2016}+1}\) và \(y=\dfrac{2016^{2016}+1}{2016^{2015}+1}\)

Answer 1

help me

Answer 2

Nếu:

\(\dfrac{a}{b}< 1\Rightarrow\dfrac{a+m}{b+m}< 1\left(m\in N\right)\)

Ta có:

\(x=\dfrac{2016^{2017}+1}{2016^{2016}+1}< 1\)

\(\Rightarrow x< \dfrac{2016^{2017}+1+2015}{2016^{2016}+1+2015}\Rightarrow x< \dfrac{2016^{2017}+2016}{2016^{2016}+2016}\Rightarrow x< \dfrac{2016\left(2016^{2016}+1\right)}{2016\left(2016^{2015}+1\right)}\Rightarrow x< \dfrac{2016^{2016}+1}{2016^{2015}+1}=y\)

\(\Rightarrow x< y\)