A complex weighted projective is $\mathbb{P}(k_1, \cdots, k_{n+1})=Proj(\mathbb{C}[x_1, \cdots, x_{n+1}])$ with $x_i$ of degree $k_i$ (sometimes people ask for each $n$ of the weights being coprime). My first question is whether all weighted projective spaces are rational.

The rationality of $\mathbb{P}(k_1, \cdots, k_{n+1})$ is equivalent to the functional field $\mathbb{C}_0(x_1, \cdots, x_{n+1})$ being free generated by $n$ elements. When $n=1$, it is clear that $\mathbb{C}_0(x_1, x_2)=\mathbb{C}(\frac{x_1^{k_2}}{x_2^{k_1}})$, hence $\mathbb{P}(k_1, k_2)$ is always a rational curve. However, I guess in higher dimension this could not hold.

If the answer to the first question is no, then my second question is that whether some weaker rationality properties, like rational connectivity, stable rationality, etc hold for weighted projective space.

Thank you in advance!