Question 58
Let $a_0 \gt 0$ be a real number, and let
$$
a_n = \frac{a_{n-1}}{\sqrt{1 + 2020 \cdot a_{n-1}^2}}, \quad \text{for } n = 1, 2, \dots, 2020.
$$
Show that $a_{2020} \lt \frac{1}{2020}$.
$$
a_n = \frac{a_{n-1}}{\sqrt{1 + 2020 \cdot a_{n-1}^2}}, \quad \text{for } n = 1, 2, \dots, 2020.
$$
Show that $a_{2020} \lt \frac{1}{2020}$.