Question 79
Let $g_{1}(x) = \frac{1}{3}(1 + x + x^{2} + \cdots)$ for all values of $x$ for which the right hand side converges. Let $g_{n}(x) = g_{1}(g_{n-1}(x))$ for all integers $n \geq 2$. What is the largest integer $r$ such that $g_{r}(x)$ is defined for some real number $x$?