Question 1 (a) Find the lim inf and lim sup of the following sequences: (i) (Cn) is an enumeration of all the rational numbers in (-V3, v2). (ii) Cn = (-1)2 (n!)2 2", n 2 1. (2n)! (b) Suppose (In) is a bounded sequence in R. Let (In, ) be a subsequence of (In). Prove that lim inf Ink _ lim inf In *-+0o and lim sup Ink