Question

Calculati suma permutarii
n
(epsilon)∑ k!*k
k=1

Answer 1

$\displaystyle\sum_{k=1}^nk!\cdot k=\displaystyle\sum_{k=1}^nk!(k+1-1)=\displaystyle\sum_{k=1}^n (k!\cdot (k+1)-k!)=\\ =\displaystyle\sum_{k=1}^n ((k+1)!-k!)=2!-1+3!-2!+\ldots +(n+1)!-n!=\\ =\boxed{(n+1)!-1}$