[SOLVED] General form of a Taylor's polynomial approx. to a multivariable function

The problem states : Find the Taylor's polynomial of degree $\displaystyle 2n$ of the function $\displaystyle f(x,y)=\frac{1}{1+xy}$ in the point $\displaystyle (0,0)$.

My attempt: I've calculated the polynomial of degree $\displaystyle 0$ and $\displaystyle 2$. ( I doubt my choice of degree $\displaystyle 0$ is a good one... but as there's no restriction over $\displaystyle n$, I can guess it is not a bad choice.)

I got that $\displaystyle P_0(0,0)=1$ and $\displaystyle P_2(0,0)=1$.

So $\displaystyle P_{2n}=1$, $\displaystyle \forall n \geq 0$.

I can't believe my result. Calculating $\displaystyle P_4(0,0)$ seems a really long work! Have I done what I've done right?