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  "body": "\n## Summary\n\nSeries acceleration uses sequence transformations to speed up a slowly converging sequence, such as the [[partial sums|09RJ859N7A]] of a series.\nThe new sequence has the same limit but converges faster.\nIt matters in numerical work, where a series may need millions of terms for a few correct digits.\nClassical methods are [[Aitken's delta-squared process|WF08BMN6Q6]], the [[Euler transform|WT0HACKQV7]], [[Richardson extrapolation|WMTZG71K2Y]], the [[Shanks transformation|C0TXDZZMH7]] and the [[Levin-type transformations|1P47PCRVTZ]].\n\n## Explanations\n\n### L1 human\n\nA slowly converging series reaches its sum only after very many terms.\nAn acceleration method looks at the pattern of the first few partial sums and guesses where they are heading.\nFor the [[Leibniz series|037FD5NBRT]] $1 - \\frac13 + \\frac15 - \\cdots = \\frac{\\pi}{4}$, the partial sums jump around $\\frac{\\pi}{4}$, and averaging neighbours already gives much better values.\nNo single method works for every sequence; each one is exact for some model of how the error behaves.\n",
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