Question

So sánh:

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

    B=\(\frac{2015^{2015}+1}{2015^{2016}+1}\)

Answer 1

\(A=\frac{2015^{2013}+1}{2015^{2014}+1}=\frac{\left(2015^{2013}+1\right)\left(2015^{2014}+1\right)}{\left(2015^{2014}+1\right)\left(2015^{2016}+1\right)}=\frac{2015^{4027}+2015^{2013}+2015^{2014}+1}{\left(2015^{2014}+1\right)\left(2015^{2016}+1\right)}\)

\(B=\frac{2015^{2015}+1}{2015^{2016}+1}=\frac{\left(2015^{2015}+1\right)\left(2015^{2014}+1\right)}{\left(2015^{2016}+1\right)\left(2015^{2014}+1\right)}=\frac{2015^{4029}+2015^{2015}+2015^{2014}+1}{\left(2015^{2016}+1\right)\left(2015^{2014}+1\right)}\)

Ta thấy hiển nhiên thử của B > tử của A nên B > A

Vậy...