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  "body": "\n## Summary\n\nZeilberger's algorithm, also called the method of creative telescoping, takes a definite sum $f(n) = \\sum_k F(n, k)$ of a hypergeometric term.\nIt finds a linear [[recurrence|0FYX44GP92]] in $n$ with polynomial coefficients that $f$ satisfies.\nIt works by running a parametrised version of [[Gosper's algorithm|NHMJQBS04M]] on a combination of shifts $F(n + j, k)$.\nWith the recurrence and a few initial values, identities for definite sums can be proved or discovered automatically.\nIt is a main tool of the \"A = B\" approach to hypergeometric identities.\n\n## Explanations\n\n### L1 human\n\nMany identities say that a sum over $k$ of binomial-like terms has a simple value depending on $n$.\nZeilberger's algorithm does not guess the value; it finds a recurrence in $n$ that the sum must satisfy.\nFor $\\sum_k \\binom{n}{k}$ it finds $f(n + 1) = 2f(n)$, and with $f(0) = 1$ this gives $2^n$.\nIf the claimed value satisfies the same recurrence and the same initial values, the identity is proved.\n",
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