Math 2.0

statement fact

Fibonacci recurrence

Statement

Let nn be a natural number, and let FmF_m be the Fibonacci numbers. Then Fn+2=Fn+1+Fn.F_{n+2} = F_{n+1} + F_n.

Remarks

With the values F0=0F_0 = 0 and F1=1F_1 = 1, the recurrence determines the whole sequence. The recurrence extends to negative indices with F−n=(−1)n+1FnF_{-n} = (-1)^{n+1} F_n.

Explanations

L1 human

To get the next Fibonacci number, add the last two. From 33 and 55 you get 88, and from 55 and 88 you get 1313.

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Sources

  1. Web https://en.wikipedia.org/wiki/Fibonacci_sequence, Definition

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