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  "body": "\n## Definition\n\nA simple continued fraction is a [[continued fraction|0BK6JBK58W]] whose partial numerators are all $1$.\nIts first term $a_0$ is an integer, and its later terms $a_1, a_2, \\dots$ are positive integers:\n$$[a_0; a_1, a_2, \\dots] = a_0 + \\cfrac{1}{a_1 + \\cfrac{1}{a_2 + \\cdots}}$$\nThe sequence of terms can be finite or infinite.\n\n## Remarks\n\nThe $a_n$ are called the partial quotients.\nFor example, $[2; 3, 4] = 2 + \\frac{1}{3 + 1/4} = \\frac{30}{13}$.\nAn infinite simple continued fraction always converges, by the [[convergence of the convergents|0E70M92FE3]].\nEach real number has a [[continued fraction expansion|0SJ7Z6VKWK]] of this form.\n\n## Explanations\n\n### L1 human\n\nA simple continued fraction is a list of integers $[a_0; a_1, a_2, \\dots]$ that encodes a number.\nTo read it, start at the end, take a reciprocal, add the next term, and repeat.\n",
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