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  "body": "\n## Definition\n\nLet $(a_n)_{n \\in \\mathbb{N}}$ be a [[real sequence|0CTV783HYT]].\nThe series with terms $a_n$ is the sequence $(s_N)_{N \\in \\mathbb{N}}$ given by\n$$s_N = a_0 + a_1 + \\cdots + a_N = \\sum_{n=0}^{N} a_n.$$\nThe notation for the series is $\\sum_{n=0}^{\\infty} a_n$, or $\\sum a_n$.\n\n## Remarks\n\nThe number $s_N$ is a [[partial sum|0NB643K60Q]] of the series.\nThe symbol $\\sum_{n=0}^{\\infty} a_n$ also denotes the [[sum of the series|0K0H5E3Z5N]], when the series is convergent. The context shows which meaning is intended.\nA series can start at another index, for example $\\sum_{n=1}^{\\infty} 1/n$.\n\n## Explanations\n\n### L1 human\n\nA series is an infinite sum $a_0 + a_1 + a_2 + \\cdots$.\nWe cannot add infinitely many numbers directly, so we add the first terms and watch what happens as we add more.\n",
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