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Continued Fractions

Mathematical expressionb0+a1b1+a2b2+a3b3+⋱{\displaystyle b_{0}+{\cfrac {a_{1}}{b_{1}+{\cfrac {a_{2}}{b_{2}+{\cfrac {a_{3}}{b_{3}+\ddots }}}}}}}An infinite continued fraction is defined by the sequences {ai},{bi}{\displaystyle \{a_{i}\},\{b_{i}\}}, for i=0,1,2,…{\displaystyle i=0,1,2,\ldots }, with a0=0{\displaystyle a_{0}=0}.A continued fraction is a mathematical expression written as a fraction whose denominator contains a sum involving another fraction, which may itself be a simple or a continued fraction.

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