MathDB
Summable set

Source: JBMO Shortlist 2006

November 10, 2008
inductionalgebra proposedalgebra

Problem Statement

Let n≥3 n\ge 3 be a natural number. A set of real numbers {x1,x2,…,xn} \{x_1,x_2,\ldots,x_n\} is called summable if \sum_{i\equal{}1}^n \frac{1}{x_i}\equal{}1. Prove that for every n≥3 n\ge 3 there always exists a summable set which consists of n n elements such that the biggest element is: a) bigger than 2^{2n\minus{}2} b) smaller than n2 n^2
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