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Sum of series/ 1/(k*(k+1)*(k+2))

Sum of series 1/(k*(k+1)*(k+2))


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  oo                   
 ___                   
 \  `                  
  \           1        
   )  -----------------
  /   k*(k + 1)*(k + 2)
 /__,                  
n = 1
$$\sum_{n=1}^{\infty} \frac{1}{k \left(k + 1\right) \left(k + 2\right)}$$ 
Sum(1/((k*(k + 1))*(k + 2)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{k \left(k + 1\right) \left(k + 2\right)}$$
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
$$a_{n} = \frac{1}{k \left(k + 1\right) \left(k + 2\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

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

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