Sum of series log(z^4)

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

True

False