IMO 2018 Shortlist A4
Let a0,a1,a2,... be a sequen e of real numbers su h that a0 “ 0, a1 “ 1, and for every n ě 2 there exists 1 ď k ď n sati...
Category: Algebra
Problem
Let a0,a1,a2,... be a sequen e of real numbers su h that a0 “ 0, a1 “ 1, and for
every n ě 2 there exists 1 ď k ď n satisfying
an “
an´1 ¨¨¨ an´k
k
.
Find the maximal possible value of a2018 ´ a2017.
(Belgium)