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Sum of series/ (k-1)*x^2+(k+4)*x+k+7

Sum of series (k-1)*x^2+(k+4)*x+k+7


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The solution

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  oo                                  
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  /   \(k - 1)*x  + (k + 4)*x + k + 7/
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n = 1
$$\sum_{n=1}^{\infty} \left(\left(k + \left(x^{2} \left(k - 1\right) + x \left(k + 4\right)\right)\right) + 7\right)$$ 
Sum((k - 1)*x^2 + (k + 4)*x + k + 7, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(k + \left(x^{2} \left(k - 1\right) + x \left(k + 4\right)\right)\right) + 7$$
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
$$a_{n} = k + x^{2} \left(k - 1\right) + x \left(k + 4\right) + 7$$
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*\7 + k + x*(4 + k) + x *(-1 + k)/
$$\infty \left(k + x^{2} \left(k - 1\right) + x \left(k + 4\right) + 7\right)$$ 
oo*(7 + k + x*(4 + k) + x^2*(-1 + k))

    Examples of finding the sum of a series

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