3) [16 marks, 4 for each part] a) Given a sequence {an }, show that if lim an = L, then lim an = L for any subsequence {anx}. b) Show that {an} converges with lim an = L if and only if both {azk } and {azk-1} converge n-too and lim azk = L = lim a2k-1. k -+0o c Let an = (-1)n+l n 2n+1 . Does {an} converge? If so find the limit and if not explain why not. d) Assume that lim an = L. Let bn = (-1)"-lan. If {bn} converges, find lim br. n-too