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