Construct a simple example where the optimal N-stage cost satisfies WN(2) lim - J* for all i, N-+0o N and yet there does not exist a w such that: WN(2) - NJ* = w(2) for all i, N. Hint: Take X = {1, 2}, U = {u}, Pui(u) = 0 for i = 1, 2. Now choose Ciy