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

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


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The solution

You have entered [src] 
  oo       
 ___       
 \  `      
  \   n - 1
   )  -----
  /     n! 
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n = 1
∑n=1∞n−1n!\sum_{n=1}^{\infty} \frac{n - 1}{n!} 
Sum((n - 1)/factorial(n), (n, 1, oo))
The radius of convergence of the power series
Given number:
n−1n!\frac{n - 1}{n!}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=n−1n!a_{n} = \frac{n - 1}{n!}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞(∣(n−1)(n+1)!n!∣n)1 = \lim_{n \to \infty}\left(\frac{\left|{\frac{\left(n - 1\right) \left(n + 1\right)!}{n!}}\right|}{n}\right)
Let's take the limit
we find
False

False
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.502
The answer [src] 
1
11 
1
Numerical answer [src] 
1.00000000000000000000000000000
1.00000000000000000000000000000
The graph
Sum of series (n-1)/factorial(n)

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