Given a sequence (an)neN, define a new sequence (a)neN by a = (an-an+1) for all n. (a) Prove that if limane, for some , then (a)neN is a null sequence. Once again, you must prove this from first principles, using the definition of convergence. (b) Give an example where the converse of (a) fails. (You should briefly justify your answer.) [00 kol