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