MathDB
Inequality over the sums - ILL 1990 MON1

Source:

September 18, 2010
inequalitiesinequalities proposed

Problem Statement

Let real numbers a1,a2,…,ana_1, a_2, \ldots, a_n satisfy 0<ai≤a, i=1,2,…,n0 < a_i \leq a, \ i = 1, 2, \ldots, n. Prove that
(i) If n=4n = 4, then 1a∑i=14ai−a1a2+a2a3+a3a4+a4a1a2≤2.\frac 1a \sum_{i=1}^4 a_i - \frac{a_1a_2 + a_2a_3 + a_3 a_4 + a_4 a_1}{a^2} \leq 2.
(ii) If n=6n = 6, then \frac 1a \sum_{i=1}^6 a_i - \frac{a_1a_2 + a_2a_3 + \cdots + a_5 a_6 + a_6 a_1}{a^2} \leq 3.$$
Back to ProblemsView on AoPS