<s>[INST] Find Solution to an infinite Nested Radicals How do I find the solution to the following:
$$ \sqrt{ 7 - \sqrt{\frac{7}{2} + \sqrt{\frac{7}{4} - \sqrt{\frac{7}{16} + \sqrt{\frac{7}{256} - \ldots}}}}}$$
I first tried looking for a pattern for the denominators, but the $16$ seems to be throwing me off. Can we use calculus in this maybe, to find limits or something?
 [/INST] Hint 1:
$$X = \sqrt{7 - \dfrac{A}{\sqrt{2}}}$$
where $A = \displaystyle\sqrt{7 + \sqrt{7 - \sqrt{7 + \sqrt{7 - ....}}}}$
Hint 2:
 $$(A^{2} - 7)^{2} = 7 - A$$
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