International Mathematics Competition
for University Students
2016

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IMC2016: Day 2, Problem 6

6. Let $(x_1,x_2,\ldots)$ be a sequence of positive real numbers satisfying ${\displaystyle \sum_{n=1}^{\infty}\frac{x_n}{2n-1}=1}$. Prove that $$ \displaystyle \sum_{k=1}^{\infty} \sum_{n=1}^{k} \frac{x_n}{k^2} \le2. $$

Proposed by Gerhard J. Woeginger, The Netherlands

        

 

IMC
2016

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