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  • Sum of series:
  • x^(4n)/n!
  • x^(n)
  • 0.4^n
  • sin(n)/n^(3/2)
  • Identical expressions

  • x^(4n)/n!
  • x to the power of (4n) divide by n!
  • x(4n)/n!
  • x4n/n!
  • x^4n/n!
  • x^(4n) divide by n!

Sum of series x^(4n)/n!



=

The solution

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