3) [16 marks, 4 for each part] a) Given a sequence {an}, show that if lim an = L, then lim any = L for any subsequence {ank}. n-too k-+0o b) Show that {an} converges with lim an = L if and only if both {azk} and {azk-1} converge and lim agx = L = lim a2k-1. k -+0o k -+0o c) Let an = (-1)n+1, 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)"-Jan. If {bn} converges, find lim on. n-too