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n numbers with different partial sums

Source: 239 2008 S8

July 28, 2020
inequalitiesn-variable inequality

Problem Statement

The natural numbers x1,x2,…,xnx_1, x_2, \ldots , x_n are such that all their 2n2^n partial sums are distinct. Prove that: x12+x22+…+xn2≥4n–13. {x_1}^2 + {x_2}^2 + \ldots + {x_n}^2 \geq \frac{4^n – 1}{3}.
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