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1/((x)(x+1)(x+2))
Sum of series/ 1/((x)(x+1)(x+2))

Sum of series 1/((x)(x+1)(x+2))


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

False
The rate of convergence of the power series
The answer [src] 
1/4
$$\frac{1}{4}$$ 
1/4
Numerical answer [src] 
0.250000000000000000000000000000
0.250000000000000000000000000000
The graph
Sum of series 1/((x)(x+1)(x+2))

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