Some Proofs About Fibonacci Numbers

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Some Proofs About Fibonacci Numbers

Nitin Verma

May 27, 2020

The Fibonacci Sequence is deﬁned as:

F1 = 1 F2 = 1 Fn = Fn− 2 + Fn− 1 ∀n > 2 (1)

So its ﬁrst few terms are:

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14
F_n	1	1	2	3	5	8	13	21	34	55	89	144	233	377

The very simple recurrence deﬁnition of the Fibonacci Sequence gives rise to many simple-structured relations among the Fibonacci Numbers. In this article we explore some of them.

All the indices and numbers referred in this article are non-negative integers unless otherwise stated.

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