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Sum of series/ 1/x^6

Sum of series 1/x^6


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The solution

You have entered [src] 
  oo     
____     
\   `    
 \     1 
  \    --
  /     6
 /     x 
/___,    
n = 10
$$\sum_{n=10}^{\infty} \frac{1}{x^{6}}$$ 
Sum(1/(x^6), (n, 10, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{x^{6}}$$
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
$$a_{n} = \frac{1}{x^{6}}$$
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
--
 6
x
$$\frac{\infty}{x^{6}}$$ 
oo/x^6

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