MathDB

A4

Part of 2018 IMO Shortlist

Problems(1)

Maximising a sequence-given value

Source: IMO Shortlist 2018 A4

7/17/2019
Let a0,a1,a2,…a_0,a_1,a_2,\dots be a sequence of real numbers such that a0=0,a1=1,a_0=0, a_1=1, and for every n≥2n\geq 2 there exists 1≤k≤n1 \leq k \leq n satisfying an=an−1+⋯+an−kk. a_n=\frac{a_{n-1}+\dots + a_{n-k}}{k}. Find the maximum possible value of a2018−a2017a_{2018}-a_{2017}.
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