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

Let X = (x_{n}) be a sequence of positive real numbers such that lim(x_{n+1}/ x_{n}) = L > 1.

Show that X is not a bounded sqeuence and hence is not convergent.

2. Relevant equations

Definition of convergence states that for every epsilon > 0 there exist some natural number K such that for all n > = K, |x_{n}- x| < epsilon, then the squence converges to x.

3. The attempt at a solution

This is a proof so there really isn't too much to say here. I have looked at the definition of convergence and I see that I can get something like x_{n+1}< x_{n}(L+e) where e is epsilon, but I do not see any way to produce an upper bound from that. I also know that the previous statement is true for all e, but that still does not seem to get me anywhere. I know I need to use the fact that L > 1, but I don't see how at this point.

Any hints, subtle or not, are welcome.

Thanks,

The Geekster

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# Homework Help: Sequences ratio test, intro to real analysis

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