Question

So sánh: 2010/2011+2011/2012+2012/2010 với 3

Help meeee!!!

Answer 1

\(\frac{2010}{2011}=\frac{2011-1}{2011}=1-\frac{1}{2011}\)

\(\frac{2011}{2012}=\frac{2012-1}{2012}=1-\frac{1}{2012}\)

\(\frac{2012}{2010}=\frac{2010+2}{2010}=1+\frac{2}{2010}\)

=> \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2010}=3+\left(\frac{2}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=3+\left(\frac{1}{2010}-\frac{1}{2011}\right)+\left(\frac{1}{2010}-\frac{1}{2012}\right)\)\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2010}=3+\frac{1}{2010.2011}+\frac{1}{2010.2012}>3\)