Problem

Source: China Northern MO 2012 p5 CNMO

Tags: Sequence, recurrence relation, algebra



Let {an} be the sequance with a0=0, an=1an12 (nN+). Select an arbitrary term ak in the sequence {an} and construct the sequence {bn}: b0=ak, bn=2bn1+1bn1 (nN+) . Determine whether the sequence {bn} is a finite sequence or an infinite sequence and give proof.