Question 6
(POL 1) Let $x_n=\sqrt[2]{2+\sqrt[3]{3+\cdots+\sqrt[n]{n}}}$. Prove that
$$x_{n+1}-x_n\lt \frac1{n!},\qquad n=2,3,\ldots.$$
$$x_{n+1}-x_n\lt \frac1{n!},\qquad n=2,3,\ldots.$$
IMO 1985 — Shortlist Question 6
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