BALTIC-WAY 2020 Problem 1

Let $a_{0}>0$ be a real number, and let

$$a_{n}=\frac{a_{n-1}}{\sqrt{1+2020 \cdot a_{n-1}^{2}}}, \text { for } n=1,2, \ldots, 2020$$

Show that $a_{2020}<\frac{1}{2020}$.