00:01
Here we're given the sum from n equals 1 to infinity of n factorial over 2n plus 3 factorial.
00:10
And we want to find out if this converges or diverges.
00:13
I think the best choice here is let's use the ratio test.
00:17
The ratio test says that we're going to plug in n plus 1.
00:20
So we're going to take the limit as n approaches infinity of plug in n plus 1.
00:25
So that's n plus 1 factorial over 2 times n plus 1 plus 3.
00:34
And then we divide by the original.
00:36
Well, when you divide by the original, that means you just multiply by flip it.
00:41
So 2n plus 3 went to the top, and n factorial goes to the bottom.
00:46
Now, the n plus 1 factorial will cancel with the n factorial, we just have an n plus 1 left over when those cancel.
00:55
Now the next one's going to be a little bit more tricky.
00:59
So let's take a look at that...