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Proof about a sequence.

  1. Feb 15, 2012 #1
    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.
  2. jcsd
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