Question 23
Let $a_{0}\gt 0$, $c\gt 0$ and
$$
a_{n+1} = \frac{a_{n} + c}{1 - a_{n} c}, \quad n = 0, 1, \ldots
$$
Is it possible that the first 1990 terms $a_{0}, a_{1}, \ldots, a_{1989}$ are all positive but $a_{1990} \lt 0$?
$$
a_{n+1} = \frac{a_{n} + c}{1 - a_{n} c}, \quad n = 0, 1, \ldots
$$
Is it possible that the first 1990 terms $a_{0}, a_{1}, \ldots, a_{1989}$ are all positive but $a_{1990} \lt 0$?