Sum of series log(i^2)

Given number:
$$\log{\left(i^{2} \right)}$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = \log{\left(i^{2} \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{\left|{\log{\left(i^{2} \right)}}\right|}{\log{\left(\left(i + 1\right)^{2} \right)}}\right)$$
Let's take the limit
we find

True

False