IMO Shortlist 2018 problem A4


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3. listopada 2019.
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Let a_0,a_1,a_2,\dots be a sequence of real numbers such that a_0=0, a_1=1, and for every n\geq 2 there exists 1\geq k \geq n satisfying a_n=\frac{a_{n-1}+\dots + a_{n-k}}{k}.Find the maximum possible value of a_{2018}-a_{2017}.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf