Question

[Lê Hoàng Bảo Thư]

So sánh:  \(A=\frac{2008}{2009}\)+ \(\frac{2009}{2010}\) + \(\frac{2010}{2016}\) và  \(B=\frac{2008+2009+2010}{2009+2010+2011}\)

Answer 1

[Thanh Tùng DZ]

Ta có :

\(B=\frac{2008+2009+2010}{2009+2010+2011}=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{20101}{2009+2010+2011}\)

Ta thấy \(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\); \(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\); 

\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)

Suy ra : A > B