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Interesting convergence of sequence

  1. Feb 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Let [itex](a_n)_{n\in\mathbb{N}}[/itex] be a real sequence such that [itex]a_0\in(0,1)[/itex] and [itex]a_{n+1}=a_n-a_n^2[/itex]
    Does [itex]\lim_{n\rightarrow\infty}na_n[/itex] exist? If yes, calculate it.

    2. Relevant equations



    3. The attempt at a solution
    I have a solution but I'd like to see other solutions..
     
  2. jcsd
  3. Feb 13, 2012 #2

    Dick

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    Homework Helper

    Asking for a solution when you haven't shown your own goes against the general spirit of the homework help forum. Try another forum if you don't want to show your own proof.
     
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