00:01
In this exercise we have the series associated to n! over n! multiplied by x! now we are going to find the interval of convergence.
00:17
To do this, let me call the general term of this sequence a n.
00:23
Here we are going to use the ratio test to determine the radius of convergence.
00:27
So we are going to compute the absolute value of a n plus 1 over a n.
00:36
Well, this guy here is going to be a n plus 1, so we are going to have n plus 1 multiplied by n! over n plus 1 multiplied by n plus 1 to the n.
00:56
Perfect! multiplied by x and multiplied by x to the n.
01:05
This is a n plus 1.
01:07
Now, over a n, so we are going to have n to the n here.
01:16
N to the n over n factorial and multiplied by x to the n.
01:24
Perfect! okay, let's simplify before we go on.
01:28
Well, we can get rid of this guy, this guy...