Fibonacci Sequence

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Definition
Fibonacci Sequence

The Fibonacci sequence is a series of numbers, starting with the pair 0 and 1, where the value of each element is calculated as the sum of the two preceding it. Hence:

[math]0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, ..., \infty[/math]

The math definition of Fibonacci Sequence is:

[math]F(0)=0, F(1)=1,\,[/math]

[math]F(n+2) = F(n + 1) + F(n)\,[/math]

The ratio of each entry in the series to its next tends toward an irrational constant, known as the Golden Ratio, whose value is approximately 1.61803398875.



Examples

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