Difference Of Nested Radicals

Calculus Level 1

S1=n+n−n+n−⋯S2=n−n+n−n+⋯\begin{aligned} S_{1}&=&\sqrt{n+\sqrt{n-\sqrt{n+\sqrt{n-\cdots}}}} \\ S_{2}&=&\sqrt{n-\sqrt{n+\sqrt{n-\sqrt{n+\cdots}}}} \end{aligned}

When both infinitely nested radicals are defined, what is S1−S2S_1 -S_2?

Matías Bruna by Matías Bruna
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