Sum of series 1/n^n

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  oo    
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\   `   
 \    1 
  \   --
  /    n
 /    n 
/___,   
n = 1

\sum_{n=1}^{\infty} \frac{1}{n^{n}}

Sum(1/(n^n), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{n^{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} = n^{- n}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(n^{- n} \left(n + 1\right)^{n + 1}\right)

False

False

The rate of convergence of the power series

The answer [src]

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 ___     
 \  `    
  \    -n
  /   n  
 /__,    
n = 1

\sum_{n=1}^{\infty} n^{- n}

Sum(n^(-n), (n, 1, oo))

Numerical answer [src]

1.29128599706266354040728259060

1.29128599706266354040728259060

The graph