Let {b,} , be the sequence defined by the following recurrence: b1 = 5 and be+1 = ,(0, + 1) for all n > 1. (a) (3 Marks) Use induction to prove that 0 1. (b) (1 Marks) Use induction to show that the sequence is increasing. Hint. Show that but - b, > 0 for all n >1. (c) (3 Marks) Conclude that {b.)2 , converges and find the value of its limit