MathDB
sum (\sqrt{x_k^2-1}}{x_{k+1}} <= 1/sqrt2 n

Source: VI Soros Olympiad 1990-00 R3 11.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 29, 2024
algebrainequalities

Problem Statement

Let n≥2 n \ge 2 and x1x_1, x2x_2, ......, xnx_n be real numbers from the segment [1,2][1,\sqrt2]. Prove that holds the inequality x12−1x2+x22−1x3+...+xn2−1x1≤22n.\frac{\sqrt{x_1^2-1}}{x_2}+\frac{\sqrt{x_2^2-1}}{x_3}+...+\frac{\sqrt{x_n^2-1}}{x_1} \le \frac{\sqrt2}{2} n.
Back to ProblemsView on AoPS