How to Calculate Fibonacci
What is Fibonacci?
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.
Step-by-Step Guide
- 1F(0) = 0, F(1) = 1
- 2F(n) = F(n-1) + F(n-2)
- 3Closed form (Binet's formula): F(n) = (φⁿ − ψⁿ) / √5
- 4φ = (1+√5)/2 ≈ 1.6180339887 (golden ratio)
Worked Examples
Input
F(10)
Result
55
0,1,1,2,3,5,8,13,21,34,55
Input
F(20)
Result
6,765
Input
F(50)
Result
12,586,269,025
About 12.6 billion
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