MathDB
sum a_i/ *s - a_i) >=n /(n-1)

Source: 1966-67 Germany R4 12.3 https://artofproblemsolving.com/community/c3208025_

October 13, 2024
algebrainequalities

Problem Statement

Prove the following theorem: If n>2n > 2 is a natural number, a1,...,ana_1, ..., a_n are positive real numbers and becomes ∑i=1nai=s\sum_{i=1}^n a_i = s, then the following holds ∑i=1nais−ai≥nn−1\sum_{i=1}^n \frac{a_i}{s - a_i} \ge \frac{n}{n - 1}
Back to ProblemsView on AoPS