Let $p\_j$ to be the $j$-th Pontryagin class of the universal $n$-plane bundle $E\_n(\mathbb{R}^\infty)\to G\_n(\mathbb{R}^\infty)$. Then according to Theorem 1.6, *The Cohomology of BSO n and BO n with Integer Coefficients, Proceedings of the American Mathematical Society 1982 Vol 85-2, Edgar H.Brown JR.*,


$H^\*(G\_n(\mathbb{R}^\infty);\mathbb{Q})=\mathbb{Q}[p\_1,p\_2,\cdots,p\_{[n/2]}]$ . 


Is there any reference giving 


$H^\*(G\_n(\mathbb{R}^{n+k});\mathbb{Q})=$ ?



rational cohomology of finite real grassmannian
In the monography "Algebraic models in geometry" by Félix, Oprea and Tanré look at section 1.12.


And also: Mimura, Mamoru and Toda, Hirosi (1991). Topology of Lie Groups. I, II, Volume 91 of Translations of Mathematical Mono- graphs. American Mathematical Society, Providence, RI. 


