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  • Sum of series:
  • n^2*x^n
  • 9/(9n^2+21n-8) 9/(9n^2+21n-8)
  • (n^3+n+5)/(n+6) (n^3+n+5)/(n+6)
  • 1/((5n-4)(5n+1)) 1/((5n-4)(5n+1))

  • Identical expressions

  • cos*pi*n/((n^ three + one)^ two)
  • co sinus of e of multiply by Pi multiply by n divide by ((n cubed plus 1) squared )
  • co sinus of e of multiply by Pi multiply by n divide by ((n to the power of three plus one) to the power of two)
  • cos*pi*n/((n3+1)2)
  • cos*pi*n/n3+12
  • cos*pi*n/((n³+1)²)
  • cos*pi*n/((n to the power of 3+1) to the power of 2)
  • cospin/((n^3+1)^2)
  • cospin/((n3+1)2)
  • cospin/n3+12
  • cospin/n^3+1^2
  • cos*pi*n divide by ((n^3+1)^2)

  • Similar expressions

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

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


∑
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The solution

You have entered [src] 
  oo           
____           
\   `          
 \    cos(pi)*n
  \   ---------
   )          2
  /   / 3    \ 
 /    \n  + 1/ 
/___,          
i = 0
$$\sum_{i=0}^{\infty} \frac{n \cos{\left(\pi \right)}}{\left(n^{3} + 1\right)^{2}}$$ 
Sum((cos(pi)*n)/(n^3 + 1)^2, (i, 0, oo))
The radius of convergence of the power series
Given number:
$$\frac{n \cos{\left(\pi \right)}}{\left(n^{3} + 1\right)^{2}}$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = - \frac{n}{\left(n^{3} + 1\right)^{2}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
  -oo*n  
---------
        2
/     3\ 
\1 + n /
$$- \frac{\infty n}{\left(n^{3} + 1\right)^{2}}$$ 
-oo*n/(1 + n^3)^2

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