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Homework Help: Determine this sequence increasing or decreasing

  1. May 7, 2012 #1
    A sequence (an) is recursively defined by a1 = 1 and
    an+1 =1 /(2+an ) for all n≥1

    I'll prove this sequence is convergent by monoton sequence theorem.ı can find ıt is bounded but ı cannot decide it is monoton because when ı write its terms,Its terms are increasing sometimes decreasing sometimes.

    How can ı prove it is increasing or decreasing?
  2. jcsd
  3. May 7, 2012 #2
    For what value of an would it be stationary, ie. an+1 = an?
  4. May 7, 2012 #3
    Do an+1-an and you'll have to combine it into one fraction and then do some factoring and you'll see if it's decreasing or increasing.
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