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[1/(ln((n+2)^3)(n+2))]
Sum of series/ [1/(ln((n+2)^3)(n+2))]

Sum of series [1/(ln((n+2)^3)(n+2))]


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  oo                       
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\   `                      
 \              1          
  \   ---------------------
  /      /       3\        
 /    log\(n + 2) /*(n + 2)
/___,                      
n = 1
$$\sum_{n=1}^{\infty} \frac{1}{\left(n + 2\right) \log{\left(\left(n + 2\right)^{3} \right)}}$$ 
Sum(1/(log((n + 2)^3)*(n + 2)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{\left(n + 2\right) \log{\left(\left(n + 2\right)^{3} \right)}}$$
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
$$a_{n} = \frac{1}{\left(n + 2\right) \log{\left(\left(n + 2\right)^{3} \right)}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 3\right) \log{\left(\left(n + 3\right)^{3} \right)}}{\left(n + 2\right) \log{\left(\left(n + 2\right)^{3} \right)}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The graph
Sum of series [1/(ln((n+2)^3)(n+2))]

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