Continued fraction

In mathematics, a continued fraction is an expression such as

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:x = a_0 + cfrac{1}{a_1 + cfrac{1}{a_2 + cfrac{1}{a_3+,cdots}}}

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where a0 is some integer and all the other numbers

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an are positive integers. Longer expressions

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are defined analogously. If the numerators are allowed to differ from unity, the resulting expression is a generalized continued fraction. For clarity, non-generalized continued fractions are also called simple continued fractions.

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