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Chisinau MO p170 1979 VIII a_{k-1}+ a_{k+1}<=2a_k

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March 17, 2021
algebrainequalitiesrecurrence relation

Problem Statement

The numbers a1,a2,...,ana_1,a_2,...,a_n ( n≥3n\ge 3) satisfy the relations a1=an=0,ak−1+ak+1≤2ak   (k=2,3,...,n−1)a_1=a_n = 0, a_{k-1}+ a_{k+1}\le 2a_k \,\,\, (k = 2, 3,..., n-1) Prove that the numbers a1,a2,...,ana_1,a_2,...,a_n are non-negative.
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