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e^(4n)

Sum of series e^(4n)



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The solution

You have entered [src]
  oo      
 ___      
 \  `     
  \    4*n
  /   E   
 /__,     
n = 1     
$$\sum_{n=1}^{\infty} e^{4 n}$$
Sum(E^(4*n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$e^{4 n}$$
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
$$x_{0} = - e$$
,
$$d = 4$$
,
$$c = 0$$
then
$$R^{4} = \tilde{\infty} \left(- e + \lim_{n \to \infty} 1\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src]
oo
$$\infty$$
oo
The graph
Sum of series e^(4n)

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