Continued Fraction
It can be expressed as the continued fraction (sequence A040002 in OEIS). The sequence of best rational approximations is:
Convergents of the continued fraction are colored; their numerators are 2, 9, 38, 161, ... (sequence A001077 in OEIS), and their denominators are 1, 4, 17, 72, ... (sequence A001076 in OEIS). The other (non-colored) terms are semiconvergents.
Read more about this topic: Square Root Of 5
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