Question

root over 2 + root 2 + root 2.......... infinity times

Answer 1

hlo mate your answer

so. Ans = 2

Answer 2

Answer:

2

Step-by-step explanation:

Given problem,

$\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.....................\infty }}}}$

Let,

$\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.....................\infty }}}}=x$

$\sqrt{2+x}=x$

$2+x=x^2$

$\implies x^2 - x - 2 =0$

$x^2 - 2x + x - 2=0$

$x(x-2)+1(x-2)=0$

$(x+1)(x-2)=0$

⇒ x = - 1  or x = 2,

x = - 1  is not possible, because value of square root of a number can not be negative,

$\implies \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.....................\infty }}}} = 2$