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Summer Clouds

21/06/2017 at 10:53
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Compare \(A=\dfrac{2011}{2012}+\dfrac{2012}{2013}\) and \(B=\dfrac{2011+2012}{2012+2013}\).




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    Phan Thanh Tinh Coordinator 21/06/2017 at 12:24

    \(A=\dfrac{2011}{2012}+\dfrac{2012}{2013}=\dfrac{2011}{2012}+\dfrac{1}{2012}+\dfrac{2012}{2013}-\dfrac{1}{2012}\)

    \(=1+\left(\dfrac{2012}{2013}-\dfrac{1}{2012}\right)\)

    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


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