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Sum of series/ (-p+5h-2,5g)*1,5n

Sum of series (-p+5h-2,5g)*1,5n


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The solution

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  oo                      
____                      
\   `                     
 \    /           5*g\    
  \   |-p + 5*h - ---|*3  
   )  \            2 /    
  /   ------------------*n
 /            2           
/___,                     
n = 1
∑n=1∞n3(−5g2+(5h−p))2\sum_{n=1}^{\infty} n \frac{3 \left(- \frac{5 g}{2} + \left(5 h - p\right)\right)}{2} 
Sum(((-p + 5*h - 5*g/2)*3/2)*n, (n, 1, oo))
The radius of convergence of the power series
Given number:
n3(−5g2+(5h−p))2n \frac{3 \left(- \frac{5 g}{2} + \left(5 h - p\right)\right)}{2}
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=n(−15g4+15h2−3p2)a_{n} = n \left(- \frac{15 g}{4} + \frac{15 h}{2} - \frac{3 p}{2}\right)
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞(nn+1)1 = \lim_{n \to \infty}\left(\frac{n}{n + 1}\right)
Let's take the limit
we find
True

False
The answer [src] 
oo*h - oo*g - oo*p
−∞g+∞h−∞p- \infty g + \infty h - \infty p 
oo*h - oo*g - oo*p

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