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evaluate \(\sqrt{2 -\!\sqrt{2 - \!\sqrt{2 - \!\sqrt{2 - \cdots}}}}\)

 Mar 14, 2020
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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)

 Mar 14, 2020

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