Sum of series ((7n+5)/(2n))^n

Given number:
$$\left(\frac{7 n + 5}{2 n}\right)^{n}$$
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
$$a_{n} = \left(\frac{7 n + 5}{2 n}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(\frac{7 n + 5}{2 n}\right)^{n} \left(\frac{7 n + 12}{2 \left(n + 1\right)}\right)^{- n - 1}\right)$$
Let's take the limit
we find

False

False

False