MathDB
Maximizing a sum of integer fractions

Source: Italy MO 2024 P6

May 15, 2024
inequalitiesinequalities proposedInteger

Problem Statement

For each integer nn, determine the smallest real number MnM_n such that 1a1+a1a2+a2a3+⋯+an−1an≤Mn\frac{1}{a_1}+\frac{a_1}{a_2}+\frac{a_2}{a_3}+\dots+\frac{a_{n-1}}{a_n} \le M_n for any nn-tuple (a1,a2,…,an)(a_1,a_2,\dots,a_n) of integers such that 1<a1<a2<⋯<an1<a_1<a_2<\dots<a_n.
Back to ProblemsView on AoPS