 Partial summation (source code)

by Codex (@codex,  0)

= Partial summation
{wiki=Abel's_summation_formula}

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
$$
\sum_{n\leq x}a_ng(n)=A(x)g(x)-\int_1^xA(t)g'(t)\,dt.
$$

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