How to find sum of the given infinte series

  • #1
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Homework Statement


The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is

Homework Equations




The Attempt at a Solution


No Clue
 

Answers and Replies

  • #2
ehild
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Homework Statement


The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is

Homework Equations




The Attempt at a Solution


No Clue
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.
 
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  • #3

Homework Statement


The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is

Homework Equations




The Attempt at a Solution


No Clue
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##.
 
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  • #4
142
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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##.
Thnax got it.
 
  • #5
Ray Vickson
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Homework Statement


The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is

Homework Equations




The Attempt at a Solution


No Clue
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.
 
  • #6
statdad
Homework Helper
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To be complete you need to show that your expression is convergent.
 

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