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China Team Selection Test 2017 TST 1 Day 1 Q2

Source: China Shanghai ,Mar 6, 2017

March 7, 2017
inequalitiesalgebraChina TST

Problem Statement

Let x>1x>1 ,nn be positive integer. Prove that∑k=1n{kx}[kx]<∑k=1n12k−1\sum_{k=1}^{n}\frac{\{kx \}}{[kx]}<\sum_{k=1}^{n}\frac{1}{2k-1} Where [kx][kx ] be the integer part of kxkx ,{kx}\{kx \} be the decimal part of kxkx.
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