\f\fConsider two sequences {h} and {mu} of SIIicIly increasing natural nmnbcrs such that [551,362. . . .] U {#31, m2. . . .} = H, Show mm 11 sequmlce of real numbers {Kn} converges in R if and only if both subsequenoe; [11.] and {gm} of {In} cmwurgc in IR and they satisfy Iim nu, = lim In.e (in which cause Ihc common limit is also the limit of the sequencc). In particular, show [hat a sequence of real numbers {.13.} conveys\" ir: R if and only if me \"even" and "odd" subsequenzes [11\"] and [13,": } hath comm-g: in R and they Satisfy lim x1' = Iim 12"-}