Let (sn) [infinity] n=1 be an enumeration of positive rational numbers in (0, 2]. This means that 0 < sn ≤ 1 is rational for every n and every positive rational number in (0, 2] appears in the sequence exactly once. (a) (4 pts) What is the set of all subsequential limits of (sn)? Justify your answer. (b) (4 pts) Find lim sup sn and lim inf sn. (c) (4 pts) What is the exact interval (end points must be discussed) of convergence of the power series X[infinity] n=1 snx n ? Justify your answer. (d) (4 pts) Does the power series X[infinity] n=1 snx n n2 represent a continuous function on [−1, 1]? Justify your answer.