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factorial(n)*n^(1/3)/(3^n+2)

  • How to use it?

  • Sum of series:
  • 8^(n-1)/factorial(n-1) 8^(n-1)/factorial(n-1)
  • factorial(n)*n^(1/3)/(3^n+2) factorial(n)*n^(1/3)/(3^n+2)
  • sqrt((2n)/(n+1)) sqrt((2n)/(n+1))
  • ln(1-1/k^2)

  • Identical expressions

  • factorial(n)*n^(one / three)/(three ^n+ two)
  • factorial(n) multiply by n to the power of (1 divide by 3) divide by (3 to the power of n plus 2)
  • factorial(n) multiply by n to the power of (one divide by three) divide by (three to the power of n plus two)
  • factorial(n)*n(1/3)/(3n+2)
  • factorialn*n1/3/3n+2
  • factorial(n)n^(1/3)/(3^n+2)
  • factorial(n)n(1/3)/(3n+2)
  • factorialnn1/3/3n+2
  • factorialnn^1/3/3^n+2
  • factorial(n)*n^(1 divide by 3) divide by (3^n+2)

  • Similar expressions

  • factorial(n)*n^(1/3)/(3^n-2)
Sum of series/ factorial(n)*n^(1/3)/(3^n+2)

Sum of series factorial(n)*n^(1/3)/(3^n+2)


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The solution

You have entered [src] 
  oo          
____          
\   `         
 \       3 ___
  \   n!*\/ n 
   )  --------
  /     n     
 /     3  + 2 
/___,         
n = 1
$$\sum_{n=1}^{\infty} \frac{\sqrt[3]{n} n!}{3^{n} + 2}$$ 
Sum((factorial(n)*n^(1/3))/(3^n + 2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sqrt[3]{n} n!}{3^{n} + 2}$$
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
$$a_{n} = \frac{\sqrt[3]{n} n!}{3^{n} + 2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\sqrt[3]{n} \left(3^{n + 1} + 2\right) \left|{\frac{n!}{\left(n + 1\right)!}}\right|}{\left(3^{n} + 2\right) \sqrt[3]{n + 1}}\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src] 
  oo          
____          
\   `         
 \    3 ___   
  \   \/ n *n!
   )  --------
  /         n 
 /     2 + 3  
/___,         
n = 1
$$\sum_{n=1}^{\infty} \frac{\sqrt[3]{n} n!}{3^{n} + 2}$$ 
Sum(n^(1/3)*factorial(n)/(2 + 3^n), (n, 1, oo))
The graph
Sum of series factorial(n)*n^(1/3)/(3^n+2)

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