n ∗ n ! + ( n − 1 ) ( n − 1 ) ! + . . . + 1 ∗ 1 ! = ( n + 1 ) ! − 1 {\displaystyle n*n!+(n-1)(n-1)!+...+1*1!=(n+1)!-1}
1 ∗ 1 ! + 2 ∗ 2 ! + 3 ∗ 3 ! + 4 ∗ 4 ! = 5 ! − 1 = 120 − 1 = 119 {\displaystyle 1*1!+2*2!+3*3!+4*4!=5!-1=120-1=119}
7 ∗ 7 ! + 6 ∗ 6 ! + . . . + 2 ∗ 2 ! + 1 = 8 ! − 1 = 40320 − 1 = 40319 {\displaystyle 7*7!+6*6!+...+2*2!+1=8!-1=40320-1=40319}