Sum of series 13n(13n+13)-(13n-13)(13+13n)

Given number:
$$13 n \left(13 n + 13\right) - \left(13 n - 13\right) \left(13 n + 13\right)$$
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
$$a_{n} = 13 n \left(13 n + 13\right) - \left(13 n - 13\right) \left(13 n + 13\right)$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{13 n \left(13 n + 13\right) - \left(13 n - 13\right) \left(13 n + 13\right)}{13 n \left(13 n + 26\right) - 13 \left(n + 1\right) \left(13 n + 26\right)}}\right|$$
Let's take the limit
we find

True

False