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  "body": "\n## Definition\n\nA [[series|0JH4MN4K1C]] $\\sum a_n$ of real numbers is divergent if it is not a [[convergent series|0CVVKY7GY2]].\nThus its sequence of partial sums has no limit in $\\mathbb{R}$.\n\n## Remarks\n\nThe series $1 + 1 + 1 + \\cdots$ diverges, and its partial sums tend to $+\\infty$.\nThe series $1 - 1 + 1 - 1 + \\cdots$ diverges, and its partial sums oscillate between $1$ and $0$.\nThe [[harmonic series|0CXTMAY5PX]] diverges, although its terms tend to $0$.\nSummation methods, such as Cesàro summation, give values to some divergent series.\n\n## Explanations\n\n### L1 human\n\nA divergent series has no sum in the usual sense.\nIts running totals grow without bound or keep jumping around.\n",
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