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

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


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo        
 ___        
 \  `       
  \    1 - n
  /   n     
 /__,       
n = 1
$$\sum_{n=1}^{\infty} n^{1 - n}$$ 
Sum(n^(1 - n), (n, 1, oo))
Numerical answer [src] 
1.62847371290158444705588914326
1.62847371290158444705588914326
The graph
Sum of series 1/n^(n-1)

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