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  "body": "\n## Definition\n\nLet $n$ be a natural number.\nThe $n$-th harmonic number is the rational number\n$$H_n = \\sum_{k=1}^{n} \\frac{1}{k} = 1 + \\frac{1}{2} + \\cdots + \\frac{1}{n}.$$\n\n## Remarks\n\nThe first values are $H_0 = 0$, $H_1 = 1$, $H_2 = 3/2$, $H_3 = 11/6$ and $H_4 = 25/12$.\nThe harmonic numbers are the partial sums of the [[harmonic series|0CXTMAY5PX]].\nThey satisfy $H_n - \\ln n \\to \\gamma$, where $\\gamma$ is the [[Euler–Mascheroni constant|00C5P9JZBK]].\n\n## Explanations\n\n### L1 human\n\nThe harmonic numbers are the running totals of $1 + 1/2 + 1/3 + \\cdots$.\nThey grow without bound, but very slowly. One needs $n = 12367$ terms to pass $10$.\n",
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