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