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Sum of series/ sqrt(n)/(n^2+i)

Sum of series sqrt(n)/(n^2+i)


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The solution

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n = 1
$$\sum_{n=1}^{\infty} \frac{\sqrt{n}}{n^{2} + i}$$ 
Sum(sqrt(n)/(n^2 + i), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sqrt{n}}{n^{2} + i}$$
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
$$a_{n} = \frac{\sqrt{n}}{n^{2} + i}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\sqrt{n} \sqrt{\left(n + 1\right)^{4} + 1}}{\sqrt{n + 1} \sqrt{n^{4} + 1}}\right)$$
Let's take the limit
we find
True

False

    Examples of finding the sum of a series

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