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(20)/(5n-3)(5n+2)
Sum of series/ (20)/(5n-3)(5n+2)

Sum of series (20)/(5n-3)(5n+2)


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The solution

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  oo                   
 ___                   
 \  `                  
  \      20            
   )  -------*(5*n + 2)
  /   5*n - 3          
 /__,                  
n = 1
∑n=1∞205n−3(5n+2)\sum_{n=1}^{\infty} \frac{20}{5 n - 3} \left(5 n + 2\right) 
Sum((20/(5*n - 3))*(5*n + 2), (n, 1, oo))
The radius of convergence of the power series
Given number:
205n−3(5n+2)\frac{20}{5 n - 3} \left(5 n + 2\right)
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=20(5n+2)5n−3a_{n} = \frac{20 \left(5 n + 2\right)}{5 n - 3}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞((5n+2)2∣15n−3∣5n+7)1 = \lim_{n \to \infty}\left(\frac{\left(5 n + 2\right)^{2} \left|{\frac{1}{5 n - 3}}\right|}{5 n + 7}\right)
Let's take the limit
we find
True

False
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.50400
The answer [src] 
oo
∞\infty 
oo
Numerical answer
The series diverges
The graph
Sum of series (20)/(5n-3)(5n+2)

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