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Convergence of a sequence

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data
    let (Xn) be a sequence in R given by X1=1 and Xn+1=1/(3+Xn) for n>=2. prove Xn converges and find the limit.


    2. Relevant equations



    3. The attempt at a solution
    well i think using the monotone convergence theorem would help but i would have to prove that the sequence is bounded and monotone. But I have not been able to prove it is monotone yet.
     
  2. jcsd
  3. Sep 5, 2011 #2

    SammyS

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    Show us your work so we can help you.

    Sometimes it helps to generate the first few terms of a sequence.
     
  4. Sep 5, 2011 #3
    X2=1/4, X3=4/13, X4=13/43, X5=43/142... the sequence kinda flips up and down. it will go down, up, down,.... it does not seem monotone...
     
  5. Sep 5, 2011 #4

    SammyS

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    How is xn+2 related to xn ?

    Then look at the subsequences, (x2n) and (x2n+1).
     
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