MathDB
sum a_i /b_i >= n where b_i is permutation of a_i

Source: Eotvos 1935 p1

September 10, 2024
algebrainequalities

Problem Statement

Let nn be a positive integer. Prove that a1b1+a2b2+...+anbn≥n\frac{a_1}{b_1}+ \frac{a_2}{b_2}+ ...+\frac{a_n}{b_n} \ge n where (b1,b2,...,bn)(b_1, b_2, ..., b_n) is any permutation of the positive real numbers a1,a2,...,ana_1, a_2, ..., a_n.
Back to ProblemsView on AoPS