Find a closed form for
$$S_n = 1 \cdot 1! + 2 \cdot 2! + \ldots + n \cdot n!.$$ for integer $n \geq 1.$ Your response should have a factorial.
Another induction problem, I tried some examples but they didn't really tell me anything.
2026-03-31 23:46:56.1775000816
Finding a Closed Form
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$$\sum_{k=1}^nkk!=(n+1)!-1$$
(Now you can accept my answer :) )