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Sum of series/ 1/(x+2)^5

Sum of series 1/(x+2)^5


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The solution

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

False
The answer [src] 
   oo   
--------
       5
(2 + x)
$$\frac{\infty}{\left(x + 2\right)^{5}}$$ 
oo/(2 + x)^5

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