1.5 A sequence an, n = 0, 1, . . . , is defined as follows. Starting with initial values a0 and a1, let an+1 = 3 2

an − 1 2

an−1, n= 1, 2, . . . .

(a) Use Cauchy’s criterion to show that the sequence converges.

(b) Find the limit of the sequence. Does the limit depend on the initial values a0 and a1?