(a) Give either a proof or a counterexample to each of the following assertions:

i. If {n un} -+ 0 as n - oo then - Un converges. ii. If {nun} - 0 as n - co then Lin=] Un converges. iii. If - Un converges then Lin=1 Un converges. iv. If - Un converges absolutely then Lin=] Un converges. v. If _ Un converges absolutely then Un