Question

So sanh A=\(\frac{2015}{2015^m}+\frac{2015}{2015^n}\)va B=\(\frac{2013}{2015^m}+\frac{2017}{2015^n}\) [m,n la cac so tu nhien khac 0]

Answer 1

\(B=\frac{215-2}{2015^m}+\frac{2015+2}{2015^n}=\frac{2015}{2015^m}-\frac{2}{2015^m}+\frac{2015}{2015^n}+\frac{2}{2015^n}=A-2\left(\frac{1}{2015^m}-\frac{1}{2015^n}\right)\)

+ Nếu \(m>n\Rightarrow2015^m>2015^n\Rightarrow\frac{2}{2015^m}<\frac{2}{2015^n}\Rightarrow\frac{2}{2015^m}-\frac{2}{2015^n}<0\Rightarrow A-\left(\frac{2}{2015^m}-\frac{2}{2015^n}\right)>A\)

=> A<B

+ Nếu

m<n làm tương tự => A>B