Given number:
$$8 i^{3} + \left(- 5 i^{2} + \left(3 - 2 i\right)\right)$$
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
$$a_{i} = 8 i^{3} - 5 i^{2} - 2 i + 3$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{\left|{8 i^{3} - 5 i^{2} - 2 i + 3}\right|}{- 2 i + 8 \left(i + 1\right)^{3} - 5 \left(i + 1\right)^{2} + 1}\right)$$
Let's take the limitwe find
True
False