Mister Exam

### Other calculators

• #### How to use it?

• 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
$$R^{4} = \infty$$
$$R = \infty$$
 / 4\
e    
$$e^{x^{4}}$$
exp(x^4)`