Sum of series 12a³k³-6a⁴k+2a6k5

Given number:
$$2 a_{6} k_{5} + \left(12 a^{3} k^{3} - 6 a^{4} k\right)$$
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
$$a_{n} = - 6 a^{4} k + 12 a^{3} k^{3} + 2 a_{6} k_{5}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find

True

False