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Let R1=2+2+2−2−2−...R_1=\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2-...}}}}} R1=2+2+2−2−2−... be a 5-periodic nested radical, with respective sign pattern is (++−−−) (++---) (++−−−).
Let R2,R3,R4,R5R_2, R_3, R_4, R_5R2,R3,R4,R5 be analogous radicals with sign patterns (−++−−) (-++--) (−++−−), (−−++−) (--++-) (−−++−), (−−−++) (---++) (−−−++), (+−−−+) (+---+) (+−−−+).
Find R1−R5+R2−R4+R3R_1-R_5+R_2-R_4+R_3R1−R5+R2−R4+R3.
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