- #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

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- #1

- 143

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Member warned about posting with no effort.

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

No Clue

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- #2

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22990atinesh said:## 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.

- #3

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Assign the entire sum as a variable.22990atinesh said:## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

No Clue

##\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##.

- #4

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Ashes Panigrahi said: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

Science Advisor

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22990atinesh said:## 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

- #6

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

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