Sum of series x^2j

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

True

False