(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

given...

3. 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?

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# Homework Help: Sequence/Induction question

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