MathDB

Suppose that the sequence

\{a_n\}

of positive reals satisfies the following conditions:
[*]

a_i \leq a_j

for every positive integers

i <j

. [*]For any positive integer

k \geq 3

, the following inequality holds:

(a_1+a_2)(a_2+a_3)\cdots(a_{k-1}+a_k)(a_k+a_1)\leq (2^k+2022)a_1a_2\cdots a_k

Prove that

\{a_n\}

is constant.

Problem Statement