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Sum of series/ (x-2)^2

Sum of series (x-2)^2


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The solution

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  oo          
 ___          
 \  `         
  \          2
  /   (x - 2) 
 /__,         
n = 1
$$\sum_{n=1}^{\infty} \left(x - 2\right)^{2}$$ 
Sum((x - 2)^2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(x - 2\right)^{2}$$
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
$$a_{n} = \left(x - 2\right)^{2}$$
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] 
           2
oo*(-2 + x)
$$\infty \left(x - 2\right)^{2}$$ 
oo*(-2 + x)^2

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