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Homework Help: Limit of converging sequence

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    a1=0 an+1=Sqrt(1+2an) n=1,2,3...

    show that an converges and find the limit

    2. Relevant equations



    3. The attempt at a solution

    I have seen something like this before but i cant remember how to solve this.

    well i think i get that it becomes sqrt(1+2sqrt(1+2sqrt(1+2sqrt) ect
    just don't know how to write it out so i can find the limit
     
  2. jcsd
  3. Feb 21, 2010 #2
    Well, to find the limit it is not that difficult actually. Both a(n+1) and a(n) approach the same limit as n tends to infinity, so its just a matter of solving a quadratic equation really.

    Takes a bit more effort to prove that it converges though *scratches head*
     
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