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1+1/factorial(n)
Sum of series/ 1+1/factorial(n)

Sum of series 1+1/factorial(n)


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The solution

You have entered [src] 
  oo          
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 \  `         
  \   /    1 \
   )  |1 + --|
  /   \    n!/
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n = 1
$$\sum_{n=1}^{\infty} \left(1 + \frac{1}{n!}\right)$$ 
Sum(1 + 1/factorial(n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$1 + \frac{1}{n!}$$
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
$$a_{n} = 1 + \frac{1}{n!}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{1 + \frac{1}{n!}}{1 + \frac{1}{\left(n + 1\right)!}}}\right|$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
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$$\infty$$ 
oo
The graph
Sum of series 1+1/factorial(n)

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