Question

B= \(\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2009}\). CM B>3

Answer 1

\(B=\frac{2009}{2010}+\frac{2010}{2011}+\frac{2009+1+1}{2009}=\frac{2009}{2010}+\frac{2010}{2011}+1+\frac{1}{2009}+\frac{1}{2009}\)

\(B=\frac{2009}{2010}+\frac{1}{2009}+\frac{2010}{2011}+\frac{1}{2009}+1\)

\(B>\frac{2009}{2010}+\frac{1}{2010}+\frac{2010}{2011}+\frac{1}{2011}+1=3\)

Answer 2

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

=> \(\frac{2009}{2010}+\frac{2010}{2011}+1+\frac{1}{2019}+\frac{1}{2019}\)

ma : + 1 - \(\frac{2009}{2010}=\frac{1}{2010}\) /// \(\frac{1}{2019}>\frac{1}{2010}\) => \(\frac{2009}{2010}+\frac{1}{2009}>1\)

+ \(1-\frac{2010}{2011}=\frac{1}{2011}\) //// \(\frac{1}{2019}>\frac{1}{2011}\) => \(\frac{1}{2019}+\frac{2010}{2011}>1\)

=> \(\left(\frac{2009}{2010}+\frac{1}{2009}\right)+\left(\frac{2010}{2011}+\frac{1}{2019}\right)+1\)

( >1 + >1 + 1 ) > 3

Dung 100%