Question 75
Let $\{a_{i}\}_{i \geq 0}$ be a sequence of real numbers defined by
$$
a_{n+1} = a_{n}^2 - \frac{1}{2^{2020 \cdot 2^{n}} - 1}
$$
for $n \geq 0$. Determine the largest value for $a_{0}$ such that $\{a_{i}\}_{i \geq 0}$ is bounded.
$$
a_{n+1} = a_{n}^2 - \frac{1}{2^{2020 \cdot 2^{n}} - 1}
$$
for $n \geq 0$. Determine the largest value for $a_{0}$ such that $\{a_{i}\}_{i \geq 0}$ is bounded.