olymmath

KöMaL 2016 C1382

    Prove the following inequality: 11+2+12+3+13+4+…+12016+2017<2017 .\frac{1}{1+\sqrt2}+\frac{1}{\sqrt2+\sqrt3}+\frac{1}{\sqrt3+\sqrt4}+\ldots +\frac{1}{\sqrt{2016}+\sqrt{2017}}< \sqrt{2017}\,.

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