00:01
Okay, we want to write the power series for 1 over 1 minus x squared and then find its radius of convergence.
00:08
So what we're going to do is we're going to use our favorite power series, g of x, which is 1 over 1 minus x, and that's equal to n equals 0 to infinity, x to the end.
00:20
Okay, and its interval of convergence is negative 1 to 1.
00:27
Okay, so what our f of x is is exactly the same as g of x, except for it has an x.
00:34
Squared plugged into it.
00:41
So n equals 0 to infinity x squared to the n or n equals 0 to infinity x to the 2n.
00:51
Can now remember on this one, what this means is that x has to be between minus 1 and 1.
01:00
So on this one, x squared has to be between minus 1 and 1.
01:06
All right, so let's look at a picture of x squared...