(4) Let {an} 1 be a positive sequence which satisfies nan+1 _ an for all n 2 1. (a) (3 Marks) Prove that an converges (you can use any convergence test). n=1 a1 (b) (3 Marks) Prove that an (n - 1) ! for all n 2 1. OO (c) (4 Marks) Given that a1 = 137 and e" = n! (for any x E R), find M so that an