MathDB
(\sum a_i )^2 >= sum a_i^3 if a_n non-decreasing, a_0 = 0,a_j-a_i<=j -i for j>1

Source: 2019 Dürer Math Competition Finals E+1.1

November 28, 2020
algebrainequalitiesSequenceSum

Problem Statement

Let ao,a1,a2,..,ana_o,a_1,a_2,..,a_ n be a non-decreasing sequence of n+1n+1 real numbers where a0=0a_0 = 0 and for every j>ij > i we have aj−ai≤j−ia_j - a_i \le j - i. Show that (∑i=0nai)2≥∑i=0nai3\left (\sum_{i=0}^n a_i \right )^2 \ge \sum_{i=0}^n a_i^3
Back to ProblemsView on AoPS