$$\sum_{n=1}^N n\cdot n!$$
I have tried to find a common factor of the terms but the only thing in common of all operands is $2!$.
2026-04-29 12:25:22.1777465522
$\sum_{n=1}^N n\cdot n!$ as a function of $N$
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Try telescoping with $n\cdot n!=(n+1)!-n!$.