A sequence xn is defined recursively by x1 = 2 and xn+1 = 8xn-1/4xn+3 for n ∈ N.
a. Prove by induction or otherwise that xn -1 > 0 for all n ∈ N.
The Attempt at a Solution
x1 is given as 2, therefore x1 - 1 = 1 > 0, which satisfies the criteria.
I'm not exactly sure how to employ induction (or the 'otherwise' method), from what I understand I need to prove that xn+1 - 1 > 0, as then the base case (n=1) and all other cases are proved... on the right track?