MathDB
n of reals

Source: 6-th Taiwanese Mathematical Olympiad 1997

January 18, 2007
inductioninequalities proposedinequalities

Problem Statement

Let n>2n>2 be an integer. Suppose that a1,a2,...,ana_{1},a_{2},...,a_{n} are real numbers such that ki=ai−1+ai+1aik_{i}=\frac{a_{i-1}+a_{i+1}}{a_{i}} is a positive integer for all ii(Here a0=an,an+1=a1a_{0}=a_{n},a_{n+1}=a_{1}). Prove that 2n≤a1+a2+...+an≤3n2n\leq a_{1}+a_{2}+...+a_{n}\leq 3n.
Back to ProblemsView on AoPS