Question Number 182506 by Matica last updated on 10/Dec/22
$$\:\:{Calculate}\:{S}\:=\:\mathrm{1}×\mathrm{1}!\:+\:\mathrm{2}×\mathrm{2}!\:+\:\mathrm{3}×\mathrm{3}!\:+\:...+\:{n}×{n}! \\ $$$$\:\:\: \\ $$
Answered by mr W last updated on 10/Dec/22
$${n}×{n}!=\left({n}+\mathrm{1}\right)!−{n}! \\ $$$$\Rightarrow{S}=\left({n}+\mathrm{1}\right)!−\mathrm{1} \\ $$
Commented by Matica last updated on 10/Dec/22
How to be a math genius like you?