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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

You have entered [src] 
  oo                      
____                      
\   `                     
 \    /           5*g\    
  \   |-p + 5*h - ---|*3  
   )  \            2 /    
  /   ------------------*n
 /            2           
/___,                     
n = 1
$$\sum_{n=1}^{\infty} n \frac{3 \left(- \frac{5 g}{2} + \left(5 h - p\right)\right)}{2}$$ 
Sum(((-p + 5*h - 5*g/2)*3/2)*n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$n \frac{3 \left(- \frac{5 g}{2} + \left(5 h - p\right)\right)}{2}$$
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
$$a_{n} = n \left(- \frac{15 g}{4} + \frac{15 h}{2} - \frac{3 p}{2}\right)$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{n}{n + 1}\right)$$
Let's take the limit
we find
True

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

    Examples of finding the sum of a series

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