Given three real numbers $a, b$ and $c$, the Gauss hypergeometric function associated with the triplet $(a, b, c)$ is defined by
$$F_{a,b,c}(x) = \sum_{n=0}^{+\infty} \frac{[a]_n [b]_n}{[c]_n} \frac{x^n}{n!}$$
Justify that, if $c \in D$, then $\frac{[a]_n [b]_n}{[c]_n}$ is well defined for any natural integer $n$.