1.4.4 For 0 < Q < 1, let I ( a ) = {z : 1 - a < z < 1 + a}. Consider a sequence

~ 1 ~ , 2. ., . o fnumbers satisfying 0 <

a, < 1 for all n, and let A, = I(a,). (i) Find lim sup A , and lim inf A,. (ii) Find conditions, expressed in terms of a,, under which lim A , exists, and find this limit. (iii) Define J ( a ) = {z : 1-0 5 z 5 l+a}

and B, = J(a,). Answer questions (i) and (ii) for sequence {B,}.