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Minimum value of sum over sequence elements

Source: IMO Shortlist 1997, Q 26

August 10, 2008
inequalitiesalgebraminimizationSequenceFibonacciIMO Shortlist

Problem Statement

For every integer n≥2 n \geq 2 determine the minimum value that the sum \sum^n_{i\equal{}0} a_i can take for nonnegative numbers a0,a1,…,an a_0, a_1, \ldots, a_n satisfying the condition a_0 \equal{} 1, a_i \leq a_{i\plus{}1} \plus{} a_{i\plus{}2} for i \equal{} 0, \ldots, n \minus{} 2.
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