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Part of 2007 Baltic Way

Problems(1)

Partitions of {1,2,3...2n} into 2-element subsets inequality

Source: Baltic Way 2007

11/30/2010
For a positive integer nn consider any partition of the set {1,2,…,2n}\{ 1,2,\ldots ,2n \} into nn two-element subsets P1,P2…,PnP_1,P_2\ldots,P_n. In each subset PiP_i, let pip_i be the product of the two numbers in PiP_i. Prove that 1p1+1p2+…+1pn<1\frac{1}{p_1}+\frac{1}{p_2}+\ldots + \frac{1}{p_n}<1
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