Question

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

Answer 1

Let us assume the whole term to be 'x'.
So,
x = √2+√2+√2+...+
Now let's square both sides and let's see what we get,
x^2 = 2+√2+√2+√2+...+
Now, we know that this series is being continued till infinity that means we can again call all the terms coming under root to be x as a whole.

x^2 = 2*(√2+√2+√2+√2+...+)
x^2 = 2x
x^2 - 2x = 0
x(x-2) = 0

So, therefore x=0 or x = 2
However, it obviously cannot be zero because that whole thing under root will surely give us some real value and not zero.

So, we neglect x = 0 and thus, x = 2 that means
√2+√2+√2+√2+...+ = 2