如何计算Fibonacci

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The Fibonacci sequence is a series where each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... The ratio of consecutive Fibonacci numbers approaches the golden ratio φ ≈ 1.618.

分步指南

1. 1F(0) = 0, F(1) = 1
2. 2F(n) = F(n-1) + F(n-2)
3. 3Closed form (Binet's formula): F(n) = (φⁿ − ψⁿ) / √5
4. 4φ = (1+√5)/2 ≈ 1.6180339887 (golden ratio)

例题解析