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Sum of series/ (i+1)*sqrt(i+2)

Sum of series (i+1)*sqrt(i+2)


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The solution

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  oo                   
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  /   (I + 1)*\/ I + 2 
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n = 4
$$\sum_{n=4}^{\infty} \left(1 + i\right) \sqrt{2 + i}$$ 
Sum((i + 1)*sqrt(i + 2), (n, 4, oo))
The radius of convergence of the power series
Given number:
$$\left(1 + i\right) \sqrt{2 + i}$$
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
$$a_{n} = \left(1 + i\right) \sqrt{2 + i}$$
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] 
     _______        
oo*\/ 2 + I *(1 + I)
$$\infty \left(1 + i\right) \sqrt{2 + i}$$ 
oo*sqrt(2 + i)*(1 + i)
Numerical answer
The series diverges

    Examples of finding the sum of a series

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