00 (2) (a) Let 0

(2) (a) Let 0 < x < and let an be a series of positive real numbers. Assume that the sequence (an)neN is decreasing and that CI'2n an for all n. Prove that the series an converges. (b) If (1) is replaced by 1 (J'2n 2 an is the result still true? Give a proof or a counterexample. (1) [10 marks] (2) [5 marks]