# 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