Question 177
Does there exist an infinite sequence of real numbers $(x_n)$ satisfying $x_1 = 2$ and
$$
\frac{2x_n^2 + 2}{x_n + 3} \lt x_{n+1} \le \frac{2x_n + 2}{x_n + 3} + 2023
$$
for all positive integers $n = 1, 2, 3, \dots$?
$$
\frac{2x_n^2 + 2}{x_n + 3} \lt x_{n+1} \le \frac{2x_n + 2}{x_n + 3} + 2023
$$
for all positive integers $n = 1, 2, 3, \dots$?