How to find sum of the given infinte series

[22990atinesh]

Homework Statement

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

Homework Equations

The Attempt at a Solution

No Clue

 

[ehild]

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.

 

[ubergewehr273]

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 $k$.

 

[22990atinesh]

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.

 

[Ray Vickson]

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.

 

[statdad]

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