Sum of series 7-4(0.6)^n

Given number:
$$7 - 4 \left(\frac{3}{5}\right)^{n}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = 7 - 4 \left(\frac{3}{5}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{4 \left(\frac{3}{5}\right)^{n} - 7}{4 \left(\frac{3}{5}\right)^{n + 1} - 7}}\right|$$
Let's take the limit
we find

True

False