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?
2026-03-29 14:56:07.1774796167
Find Solution to an infinite Nested Radicals
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Hint 1: $$X = \sqrt{7 - \dfrac{A}{\sqrt{2}}}$$ where $A = \displaystyle\sqrt{7 + \sqrt{7 - \sqrt{7 + \sqrt{7 - ....}}}}$
Hint 2: $$(A^{2} - 7)^{2} = 7 - A$$