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Algebra Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Let $f$ be a function defined on the positive integers with $f(n)\ge 0$ and $f(n)\le f(n+1)$ for all $n$ . Prove that if

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

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