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continued fraction


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An expression of the form q1+1/b2, where b2=q2+1/b3, b3=q3+1/b4, and so on, where q1, q2,…are integers, usually positive. This can be written or, in a form that is easier to print,If the continued fraction terminates, it gives a rational number. The expression of any given positive rational number as a continued fraction can be found by using the Euclidean algorithm. For example, 1274/871 is found, by using the steps which appear in the entry on the Euclidean algorithm, to equalWhen the continued fraction continues indefinitely, it represents a real number that is the limit of the sequence For example, it can be shown thatis equal to the golden ratio, and that the representation of √2 as a continued fraction is


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