MathDB

A4

Part of 2017 IMO Shortlist

Problems(1)

A sequence must be bounded

Source: IMO Shortlist 2017 A4

7/10/2018
A sequence of real numbers a1,a2,…a_1,a_2,\ldots satisfies the relation a_n=-\max_{i+j=n}(a_i+a_j)\qquad\text{for all}  n>2017. Prove that the sequence is bounded, i.e., there is a constant MM such that ∣an∣≤M|a_n|\leq M for all positive integers nn.
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