Right off, sorry for the title, couldnt think of a good one.

Suppose I have a 2 vectors vector P = [ ]'

and Q = [ ] where all of the elements in both of these vectors sum up to 1.

Prove that if a sequence of vectors satisfies

for all k = 1...n, then it must be the case that for all j. Where A_k is just some non-negative constant.