Sum of series (x-4)(x+4)

Given number:
$$\left(x - 4\right) \left(x + 4\right)$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = \left(x - 4\right) \left(x + 4\right)$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\frac{\left(x + 4\right) \left|{\frac{x - 4}{x - 3}}\right|}{x + 5}\right)$$
Let's take the limit
we find

True

False