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  "body": "\n## Summary\n\nAn indefinite sum, or antidifference, of a function $f$ is a function $F$ whose forward difference is $f$, that is $F(x + 1) - F(x) = f(x)$.\nIt plays the role for sums that an [[antiderivative|0BYWRWFT4F]] plays for integrals.\nWith an indefinite sum, every finite sum $\\sum_{k=a}^{b-1} f(k)$ becomes the difference $F(b) - F(a)$.\n\n## Explanations\n\n### L1 human\n\nSumming a sequence is the reverse of taking differences.\nIf you know a function $F$ whose steps are exactly the terms you want to add, then the total of the terms is just how far $F$ has moved.\nFor $f(x) = x$, the function $F(x) = x(x-1)/2$ works, since $F(x + 1) - F(x) = x$.\nSo $0 + 1 + \\dots + (n-1) = F(n) - F(0) = n(n-1)/2$.\n",
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