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  "body": "\n## Definition\n\nA continued fraction is given by a number $b_0$ and a finite or infinite sequence of pairs $(a_1, b_1), (a_2, b_2), \\dots$ of numbers.\nIt stands for the expression\n$$b_0 + \\cfrac{a_1}{b_1 + \\cfrac{a_2}{b_2 + \\cfrac{a_3}{b_3 + \\cdots}}}$$\nThe $a_n$ are the partial numerators and the $b_n$ are the partial denominators.\nThe $n$-th convergent is the value of the expression cut off after $(a_n, b_n)$. The value of an infinite continued fraction is the limit of its convergents, when this limit exists.\n\n## Remarks\n\nWhen $a_n = 1$ for all $n$, $b_0$ is an integer and $b_n$ is a positive integer for $n \\ge 1$, the continued fraction is a [[simple continued fraction|06XF7BCFFJ]].\nFor example, $\\sqrt{2} = 1 + \\cfrac{1}{2 + \\cfrac{1}{2 + \\cdots}}$.\nOther continued fractions give formulas for $\\pi$ and for functions such as $\\tan x$.\n\n## Explanations\n\n### L1 human\n\nA continued fraction is a fraction whose denominator contains another fraction, and so on.\nCut it off at some level, and you get an ordinary fraction. These fractions often approximate a number very well.\n",
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  "name": "Continued fraction",
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