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## Homework Statement

A sequence (X

_{n}) is defined by X

_{1}=3 and X

_{n+1}= (6X

_{n}+1)/(2X

_{n}+5) for all n[tex]\in[/tex] N.

Prove by induction or otherwise that X

_{n}-1 > 0 for all n [tex]\in[/tex] N.

## Homework Equations

## The Attempt at a Solution

I'm not sure with what to do when dealing with inequalities in an induction proof. Initial i tried subing in the recursion formula when attempting the inductive step but i dont think it gets me anywhere. I'd really appreciate any guidance on where to start.

Thanks