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Calculate-S-1-1-2-2-3-3-n-n-




Question Number 182506 by Matica last updated on 10/Dec/22
  Calculate S = 1×1! + 2×2! + 3×3! + ...+ n×n!
$$\:\:{Calculate}\:{S}\:=\:\mathrm{1}×\mathrm{1}!\:+\:\mathrm{2}×\mathrm{2}!\:+\:\mathrm{3}×\mathrm{3}!\:+\:…+\:{n}×{n}! \\ $$$$\:\:\: \\ $$
Answered by mr W last updated on 10/Dec/22
n×n!=(n+1)!−n!  ⇒S=(n+1)!−1
$${n}×{n}!=\left({n}+\mathrm{1}\right)!−{n}! \\ $$$$\Rightarrow{S}=\left({n}+\mathrm{1}\right)!−\mathrm{1} \\ $$
Commented by Matica last updated on 10/Dec/22
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