00:01
Here we're given an infinite series and we want to find a center, radius, and convergence.
00:04
And interval of convergence, sorry.
00:06
They all basically come from the same place.
00:08
Let's start off with n equals zero to infinity of negative one to the n times x minus two to the n over three to the n times n plus one.
00:18
So what i like to do is just let's go ahead and find the interval first.
00:21
Notice that we have some stuff to raise to the n.
00:23
Since there's no factorial or anything like here, that here, this is going to take over.
00:27
So as long as x minus three over two is between negative one and one, this thing is going to converge.
00:32
So that means let's multiply by three.
00:35
That's negative three is between x minus two and three...