Mister Exam

Sum of series exp(n)



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The solution

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  oo    
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 \  `   
  \    n
  /   e 
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n = 1   
$$\sum_{n=1}^{\infty} e^{n}$$
Sum(exp(n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$e^{n}$$
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
$$a_{n} = 1$$
and
$$x_{0} = - e$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(- e + \lim_{n \to \infty} 1\right)$$
Let's take the limit
we find
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 exp(n)

    Examples of finding the sum of a series