Given number:
$$\left(x - 24\right)^{n} \tan^{2}{\left(\frac{6}{\sqrt[3]{2 n}} \right)}$$
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
$$a_{n} = \tan^{2}{\left(\frac{3 \cdot 2^{\frac{2}{3}}}{\sqrt[3]{n}} \right)}$$
and
$$x_{0} = 24$$
,
$$d = 1$$
,
$$c = 1$$
then
$$R = 24 + \lim_{n \to \infty}\left(\tan^{2}{\left(\frac{3 \cdot 2^{\frac{2}{3}}}{\sqrt[3]{n}} \right)} \left|{\frac{1}{\tan^{2}{\left(\frac{3 \cdot 2^{\frac{2}{3}}}{\sqrt[3]{n + 1}} \right)}}}\right|\right)$$
Let's take the limitwe find
$$R = 25$$