Sum of series e^(4n)

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  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)

False

False

The rate of convergence of the power series

The answer [src]

oo

\infty

oo

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