My question is how we can compute the homology groups of the complex projective space $\mathbb{C}P_n$ by the following Corollary5.4 at page 31 in Milnor's book：
Corollary5.4 If $c_{\lambda+1}=c_{\lambda-1}=0$,then $R_{\lambda}=c_{\lambda}$ and $R_{\lambda+1}=R_{\lambda-1}=0$.
where $c_{\lambda}$ is the number of the critical points of index $\lambda$ of Morse function on manifold $M$,and $R_{\lambda}$ is the $\lambda$th Betti number of manifold M.
I can not firgure out the details,please give me some help! Thank you very much!