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## Homework Statement

A sequence x

_{n}is defined recursively by x

_{1}= 2 and x

_{n+1}= 8x

_{n}-1/4x

_{n}+3 for n ∈ N.

a. Prove by induction or otherwise that x

_{n}-1 > 0 for all n ∈ N.

## Homework Equations

given...

## The Attempt at a Solution

x

_{1}is given as 2, therefore x

_{1}- 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 x

_{n+1}- 1 > 0, as then the base case (n=1) and all other cases are proved... on the right track?