For every positive integer $n$, $s(n)$ denotes the sum of the digits in the decimal representation of $n$. Prove that for every integer $n \ge 5$, we have $$S(1)S(3)...S(2n-1) \ge S(2)S(4)...S(2n)$$
Problem
Source: 2021 3nd Final Mathematical Cup Junior Division P3 FMC
Tags: inequalities, number theory, sum of digits, algebra