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The Rational Number obtained by keeping only a limited number of terms in a Continued Fraction is called a convergent. For example, in the Simple Continued Fraction for the Golden Ratio,

\phi=1+{1\over\strut\displaystyle 1+{\strut\displaystyle 1\over\strut\displaystyle 1+\ldots}},

the convergents are

1, 1+{1\over 1}=2, 1+{1\over 1+{1\over 1}}={3\over 2}, \ldots.

The word convergent is also used to describe a Convergent Sequence or Convergent Series.

See also Continued Fraction, Convergent Sequence, Convergent Series, Partial Quotient, Simple Continued Fraction

© 1996-9 Eric W. Weisstein