Ta có
\(\dfrac{2010}{2011}< 1\left(1\right)\)
\(\dfrac{2011}{2012}< 1\left(2\right)\)
\(\dfrac{2012}{2013}< 1\left(3\right)\)
\(\dfrac{2013}{2014}< 1\left(4\right)\)
Từ \(\left(1\right),\left(2\right),\left(3\right)\left(4\right)\)
\(\Rightarrow\)\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}+\dfrac{2013}{2014}< 4\left(đpcm\right)\)