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Sum of series/ k^2-5*k+6

Sum of series k^2-5*k+6


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The solution

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  oo                
 ___                
 \  `               
  \   / 2          \
  /   \k  - 5*k + 6/
 /__,               
n = 1
$$\sum_{n=1}^{\infty} \left(\left(k^{2} - 5 k\right) + 6\right)$$ 
Sum(k^2 - 5*k + 6, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(k^{2} - 5 k\right) + 6$$
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
$$a_{n} = k^{2} - 5 k + 6$$
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] 
   /     2      \
oo*\6 + k  - 5*k/
$$\infty \left(k^{2} - 5 k + 6\right)$$ 
oo*(6 + k^2 - 5*k)

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