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  "body": "\n## Definition\n\nLet $\\sum a_n$ be a [[series|0JH4MN4K1C]] of real numbers with [[partial sums|0NB643K60Q]] $s_N = \\sum_{n=0}^{N} a_n$.\nThe series is convergent if the sequence $(s_N)$ is a [[convergent sequence|0AZ3R52593]].\n\n## Remarks\n\nThe series $\\sum 1/2^n$ converges, since its partial sums $2 - 1/2^N$ tend to $2$.\nThe limit of the partial sums is the [[sum of the series|0K0H5E3Z5N]].\nA series that does not converge is a [[divergent series|0NBRP6093V]].\nChanging finitely many terms does not change whether a series converges. It can change the sum.\n\n## Explanations\n\n### L1 human\n\nA series converges when its running totals approach a fixed number.\nAdding more and more terms then changes the total less and less.\n",
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  "name": "Convergent series",
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