Sum of series (x-7)^3

Given number:
$$\left(x - 7\right)^{3}$$
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
$$a_{x} = \left(x - 7\right)^{3}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\left(x - 7\right)^{2} \left|{x - 7}\right| \left|{\frac{1}{\left(x - 6\right)^{3}}}\right|\right)$$
Let's take the limit
we find

True

False