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Part of 2014 JBMO TST - Macedonia

Problems(1)

Macedonian JBMO TST 2014, Problem 1

Source:

3/30/2015
Prove that 11×2013+12×2012+13×2011+...+12012×2+12013×1<1\frac{1}{1\times2013}+\frac{1}{2\times2012}+\frac{1}{3\times2011}+...+\frac{1}{2012\times2}+\frac{1}{2013\times1}<1
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