Given number: $$\frac{n!}{n + 1}$$ 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 $$a_{n} = \frac{n!}{n + 1}$$ and $$x_{0} = 0$$ , $$d = 0$$ , $$c = 1$$ then $$1 = \lim_{n \to \infty}\left(\frac{\left(n + 2\right) \left|{\frac{n!}{\left(n + 1\right)!}}\right|}{n + 1}\right)$$ Let's take the limit we find
False
False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
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