The ∞ \infty -radical madness

Algebra Level 5

Let R1=2+2+2−2−2−...R_1=\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2-...}}}}} be a 5-periodic nested radical, with respective sign pattern is (++−−−) (++---) .

Let R2,R3,R4,R5R_2, R_3, R_4, R_5 be analogous radicals with sign patterns (−++−−) (-++--) , (−−++−) (--++-) , (−−−++) (---++) , (+−−−+) (+---+) .

Find R1−R5+R2−R4+R3R_1-R_5+R_2-R_4+R_3.

The problem is original.
Max Filippov by Max Filippov
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