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

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

  • 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
∑n=1∞(n+1)!7nn\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:
(n+1)!7nn\frac{\left(n + 1\right)!}{7^{n} n}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=(n+1)!na_{n} = \frac{\left(n + 1\right)!}{n}
and
x0=−7x_{0} = -7
,
d=−1d = -1
,
c=0c = 0
then
1R=∞~(−7+lim⁡n→∞((n+1)∣(n+1)!(n+2)!∣n))\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=0R = 0
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.50.20.5
The answer [src] 
  oo              
____              
\   `             
 \     -n         
  \   7  *(1 + n)!
  /   ------------
 /         n      
/___,             
n = 1
∑n=1∞7−n(n+1)!n\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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