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

Prove that the sequence defined by [itex] x_1=3 [/itex]

and [itex] x_{n+1}= \frac{1}{4-x_n} [/itex]

3. The attempt at a solution

Well I found like the first 4 terms of this sequence and it seems to be decreasing, heading closer to 0. So this sequence is probably bounded and if it decreasing then it will converge.

If I solve for [itex] x_n [/itex] I get that

[itex] x_n=4- \frac{1}{x_{n+1}} [/itex]

So now we see from this that the biggest [itex] x_n [/itex] could be is 4, because it seems that all our numbers are positive. I might need to use that fact that its bounded and decreasing to show that it converges.

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# Homework Help: Proof about a sequence.

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