00:01
Let's say we had a series, we'll start at one and we'll go to infinity for n plus 2x to the n.
00:12
Now this doesn't really look like it would converge.
00:15
We're going to be taking, we're going to start at one and go to n, so it looks like we're going to, well, so it's going to go to infinity when you think about it.
00:23
Let's see what happens.
00:25
Now when i see things like this, you could, i would like to try to use, i'm going to use the ratio test to try it, which seems like the limit.
00:34
So as n goes to infinity of the next term over the current term, that needs to be less than one.
00:48
And so for us, what that looks like is the limit as n goes to infinity of, now n plus 1 would be n plus 2 plus 1, which would be n plus 3x to the n plus 1, all over n plus 2x to the n.
01:12
And this needs to be less than one.
01:16
So what do we have? we, it looks like our x to the nth will cancel out and we'll just be left with x to the first power.
01:26
That's technically x minus zero to the first power.
01:31
Then we have the limit as n goes to infinity for what's left over in plus 3 over n plus 2.
01:42
That'll be less than one.
01:45
Now this limit itself, the one where n goes to infinity, the ratios or the coefficients are the same, the powers, the highest powers are the same, coefficients are the same...