Take =, NEN, and n > N and m = n +1. (2 pts) Explain why In - n+1> 6, Conclude that {n} is monotonic but it is not Cauchy. For (iii), take = 1+ (-1)". (2 pts) Show that {n} is bounded, i.e. show that [n] 2, for all n E N. . (2 pts) Compute |a- n+1l and explain why (2) cannot be a Cauchy sequence. (1 pts) For (iv) Explain why there is no example of Cauchy sequence which is not bounded (use - appropriate.result from class) la. (10 pts) Find a sequence (zn) with lim sup (zn) = 3 and lim inf (n) = -2. Justify your answer. 1b. (10 pts) Let (zn) be a bounded sequence. Show that {n} converges iff lim sup (2) lim inf (x)