Summer Clouds
21/06/2017 at 10:53-
\(A=\dfrac{2011}{2012}+\dfrac{2012}{2013}=\dfrac{2011}{2012}+\dfrac{1}{2012}+\dfrac{2012}{2013}-\dfrac{1}{2012}\)
\(=1+\left(\dfrac{2012}{2013}-\dfrac{1}{2012}\right)\)
Since \(2012^2>2013,\dfrac{2012}{2013}>\dfrac{1}{2012}\) and A > 1
\(2011< 2012< 2013\Rightarrow2011+2012< 2012+2013\Rightarrow B< 1\)
Hence,A > B