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sqrt(2)/e^(2)
Sum of series/ sqrt(2)/e^(2)

Sum of series sqrt(2)/e^(2)


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The solution

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n = 10
$$\sum_{n=10}^{\infty} \frac{\sqrt{2}}{e^{2}}$$ 
Sum(sqrt(2)/E^2, (n, 10, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sqrt{2}}{e^{2}}$$
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
$$a_{n} = \frac{\sqrt{2}}{e^{2}}$$
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 rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
Numerical answer
The series diverges
The graph
Sum of series sqrt(2)/e^(2)

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