Question

Find the value of $\sqrt{2+\sqrt{2+\sqrt{2+.....\infty }}}$

• A. $3$
• B. $2$
• C. $4$
• D. $7$

Answer 1

Answer: (B)

$2$

Let the expression be $x$

As it is extending to infinity,

Looking closely, we see that

$x=\sqrt{(2+x)}$

Squaring both sides, we get,

$x^2=2+x$

$x^2-x-2=0$

$\Rightarrow x=2,-1$

As $x$ cannot be negative, $x=2$ is correct.

Value of the expression is $2$.