MathDB

China Northern Mathematical Olympiad 2023 , Problem 4

Source: China 10 Aug

August 11, 2023

inequalitiesalgebraminimuminequalities proposed

Problem Statement

Given the sequence

(a_n)

satisfies

1=a_1< a_2 < a_3< \cdots<a_n

and there exist real number

m

such that

\displaystyle\sum_{i=1}^{n-1} \sqrt[3]{\frac{a_{i+1}-a_i}{(2+a_i)^4}}\leq m

for any positive integer

n

not less than 2 . Find the minimum of

m.