Bounding u(n) between 2/(n+2) and 4/(n+4)

Deduce that for every n ≥ 0:

   1/2 − (3/16)·u(n)  ≤  v(n+1) − v(n)  ≤  1/2

and then that

   2/(n + 2)  ≤  u(n)  ≤  4/(n + 4)

(Question II.4 of the assignment.)