Identity of dimensions related to cohomology group of projective space

Question

Let $k$ be a field, $S=k[T_0,\ldots T_r]$, $\mathbb P=\mathbb P_k^r=\operatorname{Proj}S$ and $O$ a structure sheaf of $\mathbb P$. How can I show the identity $$\operatorname{dim}_kH^0(\mathbb P,O(n))+(-1)^r\operatorname{dim}_kH^r(\mathbb P,O(n))=\binom{n+r}{r}?$$