evaluate \(\sqrt{2 -\!\sqrt{2 - \!\sqrt{2 - \!\sqrt{2 - \cdots}}}}\)
Let X represent your expression.
Since the expression is infinite in length, we can write: X = sqrt( 2 - X)
Square both sides: X2 = 2 - X
Rewrite: X2 + X - 2 = 0
Solve for X (toss away the negative value)
