I am working on a problem and stuck at some point.
We have $\displaystyle \alpha = dx_1+ \sum_{i \geq 2}^n \xi_i \ dx_i$.
I would like to calculate $(d \alpha)^{n-1}$.
In other words, what is an alternative form of $\displaystyle \left(\sum_{i=2}^n d\xi_i \ \wedge \ dx_i\right)^{n-1}$
Thanks in advance.