the first expression ist good ... r=[ρcosψ, psinψ, z] ...keep going with that ;)
next describe omega as a vector ... and calc. velocity with cross product :>
..the hint for the solution is called complete induction. ;)
First of all you starting to show that the beginning of the sequence is true.
After that you show that its also true for n+1...
Try to make some sort of attempt to solve it...