I'm currently studying with the Book "From Calculus to Cohomology" by Madsen & Tornehave(free PDF here). In the Example 18.13 there is a claim(within a calculation), that $$c((n+1)H_n^\ast) = c(H_n^\ast)^{n+1},$$ where $c$ denotes the total Chern class, $H_n$ denotes the canonical line Bundle of $\mathbb{CP}^n$ and $n\in \mathbb{N}$.
I have already understood the rest of the calculations, but somehow, I can't feel sure about this one.. maybe I just need sleep, but I need to know for certain why this is, before tomorrow morning.
My guess was, that it has something to do with the fact, that we have(18.9(ii) in the book) $$ f^\ast c_k(\xi) = c_k(f^\ast(\xi)) $$ for a complex vector bundle $\xi$.
Please punch me if I am totally wrong.. What calculation rule is causing the property above?...
I know it might be totally trivial, but please don't hesitate to state the fact, even if it's trivial af..