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  "body": "\n## Summary\n\nA summability method is a rule that assigns a value to some sequences, including some that do not converge.\nApplied to partial sums, it assigns values to some series.\nOrdinary convergence is the simplest such rule; [[Cesàro summation|N8ZGG7EW6J]], [[Abel summation|EZXPY4A19C]] and [[Borel summation|8DJPSYSHGJ]] are classical ones that extend it.\nSummability methods give useful values to [[divergent series|0JWMJSTBSG]] in analysis, number theory and physics.\nThey are studied through properties such as being [[regular|29C7C41A52]], [[linear and stable|N6Z14G81VF]].\n\n## Explanations\n\n### L1 human\n\nThe series $1 - 1 + 1 - 1 + \\cdots$ has no sum, because its partial sums jump between $1$ and $0$.\nA summability method is a different way of reading off a number from such a sequence of partial sums.\nTaking running averages, for example, gives $\\frac12$ for this series.\nDifferent methods can sum different series, and a good method should give the usual sum whenever the series converges.\n",
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