1!x1+2!x2+3!x3+.+n!xn= 1!x(2-1) + 2!x(3-1) + 3!x(4-1)+.+n!x[(n+1)-1]= (2x1!-1!) + (3x2!-2!) + (4x3!-3!) +.+ [(n+1)xn!-n!]= (2!-1!) + (3!-2!) + (4!-3!) +.+ [(n+1)!-n!]= (n+1)!-1