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sequence problem

Source: China south east mathematical olympiad 2004 day1 problem 3

June 29, 2013
logarithmsalgebrapolynomialinequalitiesalgebra unsolved

Problem Statement

(1) Determine if there exists an infinite sequence {an}\{a_n\} with positive integer terms, such that an+12≥2anan+2a^2_{n+1}\ge 2a_na_{n+2} for any positive integer nn. (2) Determine if there exists an infinite sequence {an}\{a_n\} with positive irrational terms, such that an+12≥2anan+2a^2_{n+1}\ge 2a_na_{n+2} for any positive integer nn.
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