Sum of series 14^49n2-56n-33

Given number:
$$\left(- 56 n + 144635115998316938222768918983913092176221616624719888384 n_{2}\right) - 33$$
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
$$a_{n} = - 56 n + 144635115998316938222768918983913092176221616624719888384 n_{2} - 33$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{56 n - 144635115998316938222768918983913092176221616624719888384 n_{2} + 33}{56 n - 144635115998316938222768918983913092176221616624719888384 n_{2} + 89}}\right|$$
Let's take the limit
we find

True

False