Given a sequence {a} such that a, > a > 0, and an+2 (an+1+an), for n=1,2,.... Answer the following questions: (a) Show that for n 21, (-1)" 2n an+2-an= (a-a) and hence show that the sequence (a, a3, as,) is strictly decreasing and that the sequence (az, as, ae,) is strictly increasing. (b) For any positive integers m and n, show that ama2n-1. (c) Show that the two sequences {a,, as, as,...) and (a, a, a, converge to the same limit k, where 1 k=(a +2a). 3