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How to write an algorithm to find the fibonacci series ???

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  • Computer -

    The fibonacci series is defined as the set of terms a(n)∈Z+ (i.e. all terms are integers) such that:
    a(0)=0
    a(1)=1
    a(i)=a(i-2)+a(i-1), i≥2

    The pseudocode resembles a lot the definition of the series:

    Input: n
    a(0)=0
    a(1)=1
    for i=2,i<=n,i++: a(i)=a(i-2)+a(i-1) next
    return a(n)


    Note that a closed form formula for evaluating a(n) exists, and is called the Binet's formula:
    a(n)=((p^n-(-1/p)^n)/sqrt(5)
    where p=(1+sqrt(5))/2 = the golden ratio

    However, since the result has to be an integer, and the calculations required are real, there could be rounding problems with calculations performed on a digital computer, unless symbolic algebra is available.

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