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15/((7-6n)*(1-6n))
Sum of series/ 15/((7-6n)*(1-6n))

Sum of series 15/((7-6n)*(1-6n))


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The solution

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  oo                     
 ___                     
 \  `                    
  \            15        
   )  -------------------
  /   (7 - 6*n)*(1 - 6*n)
 /__,                    
n = 2
$$\sum_{n=2}^{\infty} \frac{15}{\left(1 - 6 n\right) \left(7 - 6 n\right)}$$ 
Sum(15/(((7 - 6*n)*(1 - 6*n))), (n, 2, oo))
The radius of convergence of the power series
Given number:
$$\frac{15}{\left(1 - 6 n\right) \left(7 - 6 n\right)}$$
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
$$a_{n} = \frac{15}{\left(1 - 6 n\right) \left(7 - 6 n\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(6 n + 5\right) \left|{\frac{1}{6 n - 7}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
3*Gamma(17/6) 
--------------
11*Gamma(11/6)
$$\frac{3 \Gamma\left(\frac{17}{6}\right)}{11 \Gamma\left(\frac{11}{6}\right)}$$ 
3*gamma(17/6)/(11*gamma(11/6))
Numerical answer [src] 
0.500000000000000000000000000000
0.500000000000000000000000000000
The graph
Sum of series 15/((7-6n)*(1-6n))

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