Sum of series i^n

Given number:
$$i^{n}$$
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
$$a_{n} = 1$$
and
$$x_{0} = - i$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(- i + \lim_{n \to \infty} 1\right)$$
Let's take the limit
we find

False