On the Fibonacci Numbers
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Date
2013-02
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Addis Ababa University
Abstract
In this paper a brief history of the Fibonacci and related sequences called Lucas num-
bers will be given. Recursion formula for both sequences will also be given. A closed
formula for nth - term of Fibonacci and Lucas numbers and the relationship between
Fibonacci numbers and golden ratio will be discussed. The remaining sections will
be about finding a closed formula for the nth Fibonacci numbers by using matrix
form and its generating function. Some identities and particular theorems involving
Fibonacci sequences and identities for the common factor of Fibonacci and Lucas
numbers will be discussed. The last one will look at the occurrences of Fibonacci and
Lucas numbers in Pascals triangle.
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On the Fibonacci Numbers