# How to find sum of the given infinte series

• 22990atinesh

#### 22990atinesh

Member warned about posting with no effort.

## Homework Statement

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

## The Attempt at a Solution

No Clue

22990atinesh said:

## Homework Statement

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

## 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.

22990atinesh
22990atinesh said:

## Homework Statement

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

## 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
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.

22990atinesh said:

## Homework Statement

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

## 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.

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