Question

so sánh: C =\(\dfrac{2^{2008}-3}{2^{2007}-1}\) và D =\(\dfrac{2^{2007}-3}{2^{2006}-1}\)

Answer 1

Có:

\(\dfrac{1}{2}C=\dfrac{2^{2008}-3}{2^{2008}-2}=\dfrac{2^{2008}-2-1}{2^{2008}-2}=\dfrac{2^{2008}-2}{2^{2008}-2}-\dfrac{1}{2^{2008}-2}=1-\dfrac{1}{2^{2008}-2}\)

\(\dfrac{1}{2}D=\dfrac{2^{2007}-3}{2^{2007}-2}=\dfrac{2^{2007}-2-1}{2^{2007}-2}=\dfrac{2^{2007}-2}{2^{2007}-2}-\dfrac{1}{2^{2007}-2}=1-\dfrac{1}{2^{2007}-2}\)

\(1-\dfrac{1}{2^{2008}-2}>1-\dfrac{1}{2^{2007}-2}\Rightarrow C>D\)

Vậy \(C>D\)