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13

Part of 1962 All-Soviet Union Olympiad

Problems(1)

Sequence with Recurrent Inequality

Source: 1962 All-Soviet Union Olympiad

1/15/2018
Given are a0,a1,...,ana_0,a_1, ... , a_n, satisfying a0=an=0a_0=a_n = 0, and ak−1−2ak+ak+1≥0a_{k-1} - 2a_k+a_{k+1}\ge 0 for k=0,1,...,n−1k=0, 1, ... , n-1. Prove that all the numbers are negative or zero.
SequencealgebraRussiainequalities