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Convergence of a sequence

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data
    Check whether the sequence [itex]a_{1}=\alpha ,\alpha > 0, a_{n+1}=6*\frac{a_{n}+1}{a_{n}+7}[/itex] converges and find its limit if it does, depending on α.

    2. Relevant equations

    3. The attempt at a solution
    I showed boundedness([0,6]) and found that in the case of convergence the limit is 2, but I dont know how to check its convergence... Any help is appreciated :)
  2. jcsd
  3. Jan 27, 2014 #2
    Show it's monotone.
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