00:01
All right, we want the taylor series or the power series for this function and its radius of convergence.
00:08
Okay, so we could do it from scratch using the definition, but we don't want to do that.
00:13
So what we want to do is use a function that we know.
00:16
So let's call it g of x.
00:18
Let's call this one f of x, the one we're trying to find.
00:22
And the one that we know is 1 over 1 minus x, which is n equals 0 to infinity x to the end.
00:32
Okay, now why are we using that one? because that's the one we know.
00:37
All right.
00:38
So that's not exactly what we want because we have 1 over 1 plus 4x squared.
00:46
But if you think about that as 1 over 1 minus 4x squared, now you can see that all we have to do is plug in minus 4x squared into this function.
01:01
And we'll get the taylor series, or the power series, minus 4x squared to the n.
01:16
That gives you negative 1 to the n, 4 to the n, x to the 2n.
01:25
Okay, so that's the series...