3. (a) Let (an) be a sequence satisfying |anti - an

3. (a) Let (an) be a sequence satisfying Ian +1 anl Ian anI for all n e N \ {1}. Prove that the sequence is Cauchy. (b) Now, consider a sequence (bn) given by bn+l with bl 2 1. Using part (a), or otherwise, prove that (bn) is Cauchy. (c) Using part (b), or otherwise, prove that (bn) is convergent and find its limit explicitly. Your answer should be a function of bl. [12 marks]