Sum of series m2-n2-m-n

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

True

False