Figure-It-Out Function! - Part 6: The Second Reciprocal

Algebra Level 4

A function f(x)f(x) is such that f(1)=2f(1) = 2, f(2)=1f(2)=1, and f(x)=1f(x1)+f(x+1)f(x)=\dfrac{1}{f(x-1)+f(x+1)} for x2x \ge 2. Find

(f(2014)f(2015))(f(2012)f(2013))......(f(2)f(3))f(1)\large (f(2014)f(2015))^{(f(2012)f(2013))^{...^{...^{(f(2)f(3))^{f(1)}}}}}

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