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How to find sum of the given infinte series

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  1. Jan 10, 2015 #1
    • Member warned about posting with no effort.
    1. The problem statement, all variables and given/known data
    The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is

    2. Relevant equations


    3. The attempt at a solution
    No Clue
     
  2. jcsd
  3. Jan 10, 2015 #2

    ehild

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    Denote the limit when you do the sum and square root infinite times by A.
    ##A=\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}##.
    If you do the same once more, nothing changes
    ##A=\sqrt{12+A}##.
    Solve for A.
     
  4. Jan 10, 2015 #3
    Assign the entire sum as a variable.
    ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}} = k##
    ##\Rightarrow 12+\sqrt{12+\sqrt{12+ ...}} = k^2## ... (1)
    But,
    ##\sqrt{12+\sqrt{12+ ...}} = k## ...(2)
    Substitute (2) in (1),
    Then solve for ##k##.
     
  5. Jan 10, 2015 #4
    Thnax got it.
     
  6. Jan 12, 2015 #5

    Ray Vickson

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    Others have already shown you how. However, please realize that the above is not an infinite series. It is an infinite "something", just not a series.
     
  7. Jan 13, 2015 #6

    statdad

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    To be complete you need to show that your expression is convergent.
     
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