Given number: $$\frac{2^{n} + 3^{n}}{6^{n}}$$ 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 $$a_{n} = 2^{n} + 3^{n}$$ and $$x_{0} = -6$$ , $$d = -1$$ , $$c = 0$$ then $$\frac{1}{R} = \tilde{\infty} \left(-6 + \lim_{n \to \infty}\left(\frac{2^{n} + 3^{n}}{2^{n + 1} + 3^{n + 1}}\right)\right)$$ Let's take the limit we find