Question

SO SÁNH : A = 2015 mũ 2015 +1 / 2015 mũ 2016 + 1

                    B = 2015 mũ 2016 + 1 /2015 mũ 2017 + 1

Answer 1

Dễ dàng nhận thấy \(A=\frac{2015^{2015}+1}{2015^{2016}+1}\)cùng tử với \(B=\frac{2015^{2015}+1}{2015^{2017}+1}\)

Ta lại nhận thấy \(2015^{2016}< 2015^{2017}\)

\(\Rightarrow2015^{2016}+1< 2015^{2017}+1\)

Do đó \(\frac{2015^{2015}+1}{2015^{2016}+1}< \frac{2015^{2015}+1}{2015^{2017}+1}\) hay A < B

Answer 2

B=2015 mũ 2016/ 2015 mũ 2017 < 2015 mũ 2016+1+2014/2015 mũ 2017+1+2014 =2015×(2015 mũ 2016+1)/2015×(2015 mũ 2017+1 =2015 mũ 2015+1/ 2015 mũ 2016+1=A Vậy A