I want to compute the de Rham cohomology of the complex projective spaces $P^n_{\mathbb{C}}$. I know what the result is, and I've seen many posts in the forum asking the same thing. The problem is that, in the course I attended, we didn't deal with $CW$-complexes and I don't know what a cell decomposition is. The main tool I can use is the Mayer-Vietoris sequence.
Can you give me some tips or some references? I couldn't find anything on the internet.