MathDB

3

Part of 2004 South East Mathematical Olympiad

Problems(1)

sequence problem

Source: China south east mathematical olympiad 2004 day1 problem 3

6/29/2013
(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.
logarithmsalgebrapolynomialinequalitiesalgebra unsolved