Binet F_n=(φⁿ−ψⁿ)/√5: F₅=5, F₁₀=55; recurrence residual 0

Layer 0 — Mathematicsin the difference-and-functional-equations subtree

Sympy-exact closed-form verification of Binet's 1843 formula for the Fibonacci recurrence F_{n+2} = F_{n+1} + F_n with F_0 = 0, F_1 = 1. Characteristic polynomial λ² − λ − 1 = 0 has roots φ = (1 + √5)/2 (golden ratio) and ψ = (1 − √5)/2;…

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