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(x-6)^2
Sum of series/ (x-6)^2

Sum of series (x-6)^2


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The solution

You have entered [src] 
  oo           
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 \  `          
  \           2
  /    (x - 6) 
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x = 11
$$\sum_{x=11}^{\infty} \left(x - 6\right)^{2}$$ 
Sum((x - 6)^2, (x, 11, oo))
The radius of convergence of the power series
Given number:
$$\left(x - 6\right)^{2}$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = \left(x - 6\right)^{2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\left(x - 6\right)^{2} \left|{\frac{1}{\left(x - 5\right)^{2}}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
Numerical answer
The series diverges
The graph
Sum of series (x-6)^2

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