MathDB

2

Part of 2021 Canada National Olympiad

Problems(1)

Canadian MO 2021 P2

Source:

3/12/2021
Let n≥2n\geq 2 be some fixed positive integer and suppose that a1,a2,…,ana_1, a_2,\dots,a_n are positive real numbers satisfying a1+a2+⋯+an=2n−1a_1+a_2+\cdots+a_n=2^n-1.
Find the minimum possible value of a11+a21+a1+a31+a1+a2+⋯+an1+a1+a2+⋯+an−1\frac{a_1}{1}+\frac{a_2}{1+a_1}+\frac{a_3}{1+a_1+a_2}+\cdots+\frac{a_n}{1+a_1+a_2+\cdots+a_{n-1}}
algebrainequalitiesCMOCanadan-variable inequality