How to find sum of the given infinte series

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1. Jan 10, 2015

22990atinesh

• 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. Jan 10, 2015

ehild

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. Jan 10, 2015

Ashes Panigrahi

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 $k$.

4. Jan 10, 2015

22990atinesh

Thnax got it.

5. Jan 12, 2015

Ray Vickson

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. Jan 13, 2015