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  • Similar expressions

  • 2/(x^2-2x)
Sum of series/ 2/(x^2+2x)

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


∑
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The solution

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

    Examples of finding the sum of a series

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