## Divergence of a vector field through a symplectic 2-form

Hi everyone.

I have the following problem: i have a symplectic $(M,\omega)$ of dimension 2n, and a symplectic connection $\nabla$ that is of the Ricci-type. I need to proof that for any vectorfield $X$: $$\mathrm{div}X\omega^n:={L}_X \omega^n=\mathrm{Trace}[Z\rightarrow \nabla_Z X]\omega^n.$$

I was able to proof that $$\mathcal{L}_X \omega^n=n(\omega(\nabla_. X, .)+\omega(.,\nabla_. X))\wedge \omega^{n-1},$$ but I got stuck there.