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Putnam 1978 B6

Source: Putnam 1978

May 2, 2022
PutnamSummationinequalities

Problem Statement

Let pp and nn be positive integers. Suppose that the numbers chkc_{hk} (h=1,2,…,nh=1,2,\ldots,n ; k=1,2,…,phk=1,2,\ldots,ph) satisfy 0≤chk≤1.0 \leq c_{hk} \leq 1. Prove that (∑chkh)2≤2p∑chk, \left( \sum \frac{ c_{hk} }{h} \right)^2 \leq 2p \sum c_{hk} , where each summation is over all admissible ordered pairs (h,k).(h,k).
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