The \( \infty \)-radical madness
Algebra
Level
5
Let \[R_1=\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2-...}}}}} \] be a 5-periodic nested radical, with respective sign pattern is \( (++---) \).
Let \(R_2, R_3, R_4, R_5\) be analogous radicals with sign patterns \( (-++--) \), \( (--++-) \), \( (---++) \), \( (+---+) \).
Find \(R_1-R_5+R_2-R_4+R_3\).
The problem is original.
by
Max Filippov