Calculadora de la Secuencia de Fibonacci
Calcula cualquier término de la secuencia de Fibonacci al instante. Ingresa la posición y obtén el número de Fibonacci correspondiente de forma gratuita.
Fib N
55
Fórmula
Fibonacci Sequence
Definition
F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2)
Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Binet's Formula
F(n) = (phi^n - psi^n) / sqrt(5)
where phi = (1 + sqrt(5))/2 (golden ratio) and psi = (1 - sqrt(5))/2.
For large n, psi^n approaches 0, so F(n) ≈ phi^n / sqrt(5).
Golden Ratio
As n grows, F(n)/F(n-1) approaches the golden ratio phi ≈ 1.6180339887.
Ejemplo Resuelto
Find the 10th Fibonacci number.
- 01F(10) = phi^10 / √5
- 02= 1.61803^10 / 2.23607
- 03≈ 122.992 / 2.236
- 04≈ 55
- 05Sequence up to F(10): 0,1,1,2,3,5,8,13,21,34,55
Preguntas Frecuentes
What is the Fibonacci sequence?
The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
What is the golden ratio?
The golden ratio (phi ≈ 1.618) is the limit of the ratio of consecutive Fibonacci numbers. It appears in art, architecture, and nature.
Where do Fibonacci numbers appear in nature?
Fibonacci numbers appear in flower petals, seed spirals in sunflowers, pinecones, pineapples, and branching patterns in trees.
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