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e^n/n^10

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  • Sum of series:
  • 3i
  • e^n/n^10 e^n/n^10
  • n^2*x^n
  • n^3 n^3

  • Identical expressions

  • e^n/n^ ten
  • e to the power of n divide by n to the power of 10
  • e to the power of n divide by n to the power of ten
  • en/n10
  • e^n divide by n^10
Sum of series/ e^n/n^10

Sum of series e^n/n^10


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The solution

You have entered [src] 
  oo     
____     
\   `    
 \      n
  \    E 
   )  ---
  /    10
 /    n  
/___,    
n = 1
$$\sum_{n=1}^{\infty} \frac{e^{n}}{n^{10}}$$ 
Sum(E^n/n^10, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{e^{n}}{n^{10}}$$
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
$$a_{n} = \frac{1}{n^{10}}$$
and
$$x_{0} = - e$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(- e + \lim_{n \to \infty}\left(\frac{\left(n + 1\right)^{10}}{n^{10}}\right)\right)$$
Let's take the limit
we find
False
The rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
The graph
Sum of series e^n/n^10

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