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factorial(n+1)/((7^n*n))

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  • Sum of series:
  • factorial(n+1)/((7^n*n)) factorial(n+1)/((7^n*n))
  • sin^2(1/4n) sin^2(1/4n)
  • sin(nx)/n^2
  • 1/((3n-2)*(3n+1)) 1/((3n-2)*(3n+1))

  • Identical expressions

  • factorial(n+ one)/((seven ^n*n))
  • factorial(n plus 1) divide by ((7 to the power of n multiply by n))
  • factorial(n plus one) divide by ((seven to the power of n multiply by n))
  • factorial(n+1)/((7n*n))
  • factorialn+1/7n*n
  • factorial(n+1)/((7^nn))
  • factorial(n+1)/((7nn))
  • factorialn+1/7nn
  • factorialn+1/7^nn
  • factorial(n+1) divide by ((7^n*n))

  • Similar expressions

  • factorial(n-1)/((7^n*n))
Sum of series/ factorial(n+1)/((7^n*n))

Sum of series factorial(n+1)/((7^n*n))


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The solution

You have entered [src] 
  oo          
____          
\   `         
 \    (n + 1)!
  \   --------
  /      n    
 /      7 *n  
/___,         
n = 1
$$\sum_{n=1}^{\infty} \frac{\left(n + 1\right)!}{7^{n} n}$$ 
Sum(factorial(n + 1)/((7^n*n)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\left(n + 1\right)!}{7^{n} n}$$
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
$$a_{n} = \frac{\left(n + 1\right)!}{n}$$
and
$$x_{0} = -7$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-7 + \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{\frac{\left(n + 1\right)!}{\left(n + 2\right)!}}\right|}{n}\right)\right)$$
Let's take the limit
we find
False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
  oo              
____              
\   `             
 \     -n         
  \   7  *(1 + n)!
  /   ------------
 /         n      
/___,             
n = 1
$$\sum_{n=1}^{\infty} \frac{7^{- n} \left(n + 1\right)!}{n}$$ 
Sum(7^(-n)*factorial(1 + n)/n, (n, 1, oo))
Numerical answer
The series diverges
The graph
Sum of series factorial(n+1)/((7^n*n))

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