5. Let k > O and :11 be a positive number. Dene a sequence {an} by the relation: an\" = Vk+an for n2 1. Let 0: be the positive root of the equation: 3:2 a: k = 0. (a) Suppose 0 or. Show that the sequence {an} is monotonic decreasing and converges to or. 6. Given a sequence {an} such that :11 > (12 > O, and 1 an+2 = (an+1 +13\"), for n = 1323'\" ' Answer the following questions: (a) Show that for n 2 1, (1)n 211 an\" an = ((11 (12) and hence show that the sequence {a1,a3,a5, - - } is strictly decreasing and that the sequence {(12, a4, a5, - - - } is strictly increasing. (b) For any positive integers m and n, show that 32m R, where f(:1?) = (c) f : R) R, where f(3:) = f/E. (d) f : [1,1] > [0,4), where f(a:) = 3:2. 3321 zit1