Find the value of:

Posted June 14th, 2008 by alpha

Find the value of :

$\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+....................\infty}}}}$

Show me all the steps.
Thank you

Comments

On June 15th, 2008 alpha says:

This is a very interesting question.Please help me .I have no idea about solving this question.This looks very scary to me.

On June 19th, 2008 Structure says:

$x_n=\sqrt{6+\sqrt{6+\sqrt{6+...\sqrt 6}}}=\sqrt{6+x_{n-1}$

$x_n^2=6+x_{n-1}$

This is a convergent sequence so has a limit.
Taking the limit you have

$l^2=6+l$

Positive solution is l=3
so the symbol you ask about is 3.