$\mathbb{P}^n = \mathbb{A}^{n}⊔\mathbb{A}^{n-1}⊔\mathbb{A}^{n-2}⊔...⊔ \mathbb{A}^{2}⊔\mathbb{A}^{1}⊔\mathbb{A}^{0} $
Use this decomposition to give a formula for the number of points of $\mathbb{P}^n$ over $\mathbb{F}_p$, where $p$ is a prime number.
Is the number of points $= p^n + p^{n-1} + p^{n-2} +...+ p^2 +p^1 +p^0$?