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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.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.Homework Statement
The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is
Homework Equations
The Attempt at a Solution
No Clue
Thnax got it.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##.
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.Homework Statement
The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is
Homework Equations
The Attempt at a Solution
No Clue