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(1-1/n)^(n^2)

  • How to use it?

  • Sum of series:
  • (1+1/n)^(n^2) (1+1/n)^(n^2)
  • x*1,2^n
  • 15/((7-6n)*(1-6n)) 15/((7-6n)*(1-6n))
  • sin(n)/n^3 sin(n)/n^3
  • Limit of the function:
  • (1-1/n)^(n^2) (1-1/n)^(n^2)

  • Identical expressions

  • (one - one /n)^(n^ two)
  • (1 minus 1 divide by n) to the power of (n squared )
  • (one minus one divide by n) to the power of (n to the power of two)
  • (1-1/n)(n2)
  • 1-1/nn2
  • (1-1/n)^(n²)
  • (1-1/n) to the power of (n to the power of 2)
  • 1-1/n^n^2
  • (1-1 divide by n)^(n^2)

  • Similar expressions

  • (1+1/n)^(n^2)
Sum of series/ (1-1/n)^(n^2)

Sum of series (1-1/n)^(n^2)


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The solution

You have entered [src] 
  oo             
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 \           / 2\
  \          \n /
   )  /    1\    
  /   |1 - -|    
 /    \    n/    
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n = 1
$$\sum_{n=1}^{\infty} \left(1 - \frac{1}{n}\right)^{n^{2}}$$ 
Sum((1 - 1/n)^(n^2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(1 - \frac{1}{n}\right)^{n^{2}}$$
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
$$a_{n} = \left(1 - \frac{1}{n}\right)^{n^{2}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(1 - \frac{1}{n + 1}\right)^{- \left(n + 1\right)^{2}} \left|{\left(1 - \frac{1}{n}\right)^{n^{2}}}\right|\right)$$
Let's take the limit
we find
False

False

False
The rate of convergence of the power series
Numerical answer [src] 
0.104556251724813703737068273536
0.104556251724813703737068273536
The graph
Sum of series (1-1/n)^(n^2)

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