Question 70
Let $(a_n)$ be a sequence of positive real numbers such that for all $n \gt 2025$ we have
$$
a_n = \max_{1 \le i \le 2025} a_{n-i} - \min_{1 \le i \le 2025} a_{n-i}
$$
Prove that there is a positive integer $M$ such that $a_n \lt \frac{1}{1404}$, for all $n \gt M$.
$$
a_n = \max_{1 \le i \le 2025} a_{n-i} - \min_{1 \le i \le 2025} a_{n-i}
$$
Prove that there is a positive integer $M$ such that $a_n \lt \frac{1}{1404}$, for all $n \gt M$.