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double sum t_it_j |s_i-s_j| < = 0

Source: Polish MO Second Round 1974 p2

September 8, 2024
algebraSuminequalities

Problem Statement

Prove that for every n=2,3,… n = 2, 3, \ldots and any real numbers t1,t2,…,tn t_1, t_2, \ldots, t_n , s1,s2,…,sn s_1, s_2, \ldots, s_n , if ∑i=1nti=0, to ∑i=1n∑j=1ntitj∣si−sj∣≤0. \sum_{i=1}^n t_i = 0, \text{ to } \sum_{i=1}^n\sum_{j=1}^n t_it_j |s_i-s_j| \leq 0.
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