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24/((5-3n)(2-3n))
Sum of series/ 24/((5-3n)(2-3n))

Sum of series 24/((5-3n)(2-3n))


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The solution

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  oo                     
 ___                     
 \  `                    
  \            24        
   )  -------------------
  /   (5 - 3*n)*(2 - 3*n)
 /__,                    
n = 4
$$\sum_{n=4}^{\infty} \frac{24}{\left(2 - 3 n\right) \left(5 - 3 n\right)}$$ 
Sum(24/(((5 - 3*n)*(2 - 3*n))), (n, 4, oo))
The radius of convergence of the power series
Given number:
$$\frac{24}{\left(2 - 3 n\right) \left(5 - 3 n\right)}$$
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
$$a_{n} = \frac{24}{\left(2 - 3 n\right) \left(5 - 3 n\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(3 n + 1\right) \left|{\frac{1}{3 n - 5}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
12*Gamma(13/3)
--------------
35*Gamma(10/3)
$$\frac{12 \Gamma\left(\frac{13}{3}\right)}{35 \Gamma\left(\frac{10}{3}\right)}$$ 
12*gamma(13/3)/(35*gamma(10/3))
Numerical answer [src] 
1.14285714285714285714285714286
1.14285714285714285714285714286
The graph
Sum of series 24/((5-3n)(2-3n))

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