Given number:
$$2 \left(\left(5 n + \frac{1}{n^{3}}\right) + 6\right)$$
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
$$a_{n} = 10 n + 12 + \frac{2}{n^{3}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{10 n + 12 + \frac{2}{n^{3}}}{10 n + 22 + \frac{2}{\left(n + 1\right)^{3}}}\right)$$
Let's take the limitwe find
True
False