Question 9
Let
$$
F(x) = \frac{1}{\left(2 - x - x^{5}\right)^{2011}},
$$
and note that $F$ may be expanded as a power series so that $F(x) = \sum_{n=0}^{\infty} a_n x^n$. Find an ordered pair of positive real numbers $(c, d)$ such that
$$
\lim_{n \rightarrow \infty} \frac{a_n}{n^d} = c.
$$
$$
F(x) = \frac{1}{\left(2 - x - x^{5}\right)^{2011}},
$$
and note that $F$ may be expanded as a power series so that $F(x) = \sum_{n=0}^{\infty} a_n x^n$. Find an ordered pair of positive real numbers $(c, d)$ such that
$$
\lim_{n \rightarrow \infty} \frac{a_n}{n^d} = c.
$$