Difference Of Nested Radicals
Calculus
Level
1
\[\begin{eqnarray} S_{1}&=&\sqrt{n+\sqrt{n-\sqrt{n+\sqrt{n-\cdots}}}} \\ S_{2}&=&\sqrt{n-\sqrt{n+\sqrt{n-\sqrt{n+\cdots}}}} \end{eqnarray} \]
When both infinitely nested radicals are defined, what is \(S_1 -S_2\)?
by
Matías Bruna