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6n(n-1)/(10000)^3
Sum of series/ 6n(n-1)/(10000)^3

Sum of series 6n(n-1)/(10000)^3


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The solution

You have entered [src] 
  oo               
 ___               
 \  `              
  \    6*n*(n - 1) 
   )  -------------
  /   1000000000000
 /__,              
n = 1
$$\sum_{n=1}^{\infty} \frac{6 n \left(n - 1\right)}{1000000000000}$$ 
Sum(((6*n)*(n - 1))/1000000000000, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{6 n \left(n - 1\right)}{1000000000000}$$
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
$$a_{n} = \frac{3 n \left(n - 1\right)}{500000000000}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left|{n - 1}\right|}{n + 1}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
Numerical answer
The series diverges
The graph
Sum of series 6n(n-1)/(10000)^3

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