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prod (1+a_k^2 / a_{k+1}) > = prod (1+a_k)

Source: TOT 438 1994 Autumn A S4 - Tournament of Towns

June 12, 2024
algebrainequalities

Problem Statement

Prove that for all positive a1.a2,...,ana_1. a_2, ..., a_n the inequality (1+a12a2)(1+a22a3)...(1+an2a1)≥(1+a1)(1+a2)...(1+an)\left( 1+\frac{a_1^2}{a_2}\right) \left( 1+\frac{a_2^2}{a_3}\right) ...\left( 1+\frac{a_n^2}{a_1}\right) \ge (1+a_1)(1+a_2)...(1+a_n) holds.
(LD Kurliandchik)
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