Given number: $$f x$$ It is a series of species $$a_{x} \left(c x - x_{0}\right)^{d x}$$ - power series. The radius of convergence of a power series can be calculated by the formula: $$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$ In this case $$a_{x} = f x$$ and $$x_{0} = 0$$ , $$d = 0$$ , $$c = 1$$ then $$1 = \lim_{x \to \infty}\left(\frac{x}{x + 1}\right)$$ Let's take the limit we find