Question

so sánh 2 phân số

A= 2004^2003 +1 / 2004^2004 +1

B=2004^2002+1/2004^2003 +1

Answer 1

Ta có: \(2004A=\dfrac{2004^{2004}+2004}{2004^{2004}+1}=1+\dfrac{2003}{2004^{2004}+1}\)

\(2004B=\dfrac{2004^{2003}+2004}{2004^{2003}+1}=1+\dfrac{2003}{2004^{2003}+1}\)

Vì \(\dfrac{2003}{2004^{2004}+1}< \dfrac{2003}{2004^{2003}+1}\Rightarrow1+\dfrac{2003}{2004^{2004}+1}< 1+\dfrac{2003}{2004^{2003}+1}\)

\(\Rightarrow2004A< 2004B\)

\(\Rightarrow A< B\)

Vậy A < B