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Infinite series

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    What does the series converge to?
    [a1]=√12
    [an+1]=√(12+an)


    2. Relevant equations
    Let L = the limit it approaches


    3. The attempt at a solution
    I don't know if i did this correctly but I made
    L = √(12+√(12+√(12+...)))
    then L2 = 12+√(12+√(12+...))
    then L = 12 + 12∞-1...12
    thus L = ∞√(12 + 12∞-1...12)
     

    Attached Files:

  2. jcsd
  3. Dec 7, 2011 #2

    Dick

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    If it converges then a_n approaches L as n->infinity. So does a_(n+1). Put that into a_n=sqrt(12+a_(n+1)).
     
  4. Dec 7, 2011 #3
    ok i get that an+1 converges now because it is in the an series, but what is the limit that it approaches?
     
  5. Dec 7, 2011 #4

    Dick

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    It approaches the same limit as a_n, call it L. Solve for L!
     
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