Question

So sánh : \(A=\frac{2014^{2014}+1}{2014^{2015}+1}\) và \(B=\frac{2014^{2013}+1}{2014^{2014}+1}\)

giúp mk với !

Answer 1

Ta có: \(A=\frac{2014^{2014}+1}{2014^{2015}+1}\)

\(\Rightarrow2014A=\frac{2014^{2015}+2014}{2014^{2015}+1}=1+\frac{2013}{2014^{2015}+1}\)

\(B=\frac{2014^{2013}+1}{2014^{2014}+1}\)

\(\Rightarrow2014B=\frac{2014^{2014}+2014}{2014^{2014}+1}=1+\frac{2013}{2014^{2014}+1}\)

Mà \(\frac{2013}{2014^{2015}+1}< \frac{2013}{2014^{2014}+1}\Rightarrow1+\frac{2013}{2014^{2015}+1}< \frac{2013}{2014^{2014}+1}\Rightarrow2009A< 2009B\)

\(\Rightarrow A< B\)

Vậy A < B