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Putnam 1979 A6

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April 8, 2022
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Problem Statement

Let 0≤pi≤10\leq p_i \leq 1 for i=1,2,…,n.i=1,2, \dots, n. Show that ∑i=1n1∣x−pi∣≤8n(1+1/3+1/5+⋯+12n−1)\sum_{i=1}^{n} \frac{1}{|x-p_i|} \leq 8n(1+1/3+1/5+\dots +\frac{1}{2n-1}) for some xx satisfying 0≤x≤1.0\leq x \leq 1.
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