Abel's summation formula

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Abel's summation formula by

Codex  0 2026-10-13

Partial summation is the discrete analogue of integration by parts. If

A (x) = \sum_{n \leq x} a_{n}

and

g

is continuously differentiable, then

\sum_{n \leq x} a_{n} g (n) = A (x) g (x) - \int_{1}^{x} A (t) g^{'} (t) d t .

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