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  • Sum of series:
  • sin(n) sin(n)
  • (-1)^n/sqrt(n) (-1)^n/sqrt(n)
  • 4!^2(i-1)/n^4
  • 2*n^2/12544 2*n^2/12544

  • Identical expressions

  • four !^ two (i- one)/n^ four
  • 4! squared (i minus 1) divide by n to the power of 4
  • four ! to the power of two (i minus one) divide by n to the power of four
  • 4!2(i-1)/n4
  • 4!2i-1/n4
  • 4!²(i-1)/n⁴
  • 4! to the power of 2(i-1)/n to the power of 4
  • 4!^2i-1/n^4
  • 4!^2(i-1) divide by n^4

  • Similar expressions

  • 4!^2(i+1)/n^4
Sum of series/ 4!^2(i-1)/n^4

Sum of series 4!^2(i-1)/n^4


∑
=

The solution

You have entered [src] 
  oo             
____             
\   `            
 \      2        
  \   4! *(i - 1)
   )  -----------
  /         4    
 /         n     
/___,            
i = 1
∑i=1∞(i−1)4!2n4\sum_{i=1}^{\infty} \frac{\left(i - 1\right) 4!^{2}}{n^{4}} 
Sum((factorial(4)^2*(i - 1))/n^4, (i, 1, oo))
The radius of convergence of the power series
Given number:
(i−1)4!2n4\frac{\left(i - 1\right) 4!^{2}}{n^{4}}
It is a series of species
ai(cx−x0)dia_{i} \left(c x - x_{0}\right)^{d i}
- power series.
The radius of convergence of a power series can be calculated by the formula:
Rd=x0+lim⁡i→∞∣aiai+1∣cR^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}
In this case
ai=576i−576n4a_{i} = \frac{576 i - 576}{n^{4}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡i→∞(∣576i−576∣576i)1 = \lim_{i \to \infty}\left(\frac{\left|{576 i - 576}\right|}{576 i}\right)
Let's take the limit
we find
True

False
The answer [src] 
oo
--
 4
n
∞n4\frac{\infty}{n^{4}} 
oo/n^4

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