Question 28
Let $c \gt 0$ be a positive real number. We define the sequence $(x_n)$ by $x_0 = 0$ and
$$
x_{n+1} = x_n^2 + c
$$
for each $n \geq 0$. For which values of $c$ is it true that $|x_n| \lt 2016$ for all $n$?
$$
x_{n+1} = x_n^2 + c
$$
for each $n \geq 0$. For which values of $c$ is it true that $|x_n| \lt 2016$ for all $n$?