Hello,
[tex] x_{1} =1*1!=1\\
x_{2} =2*2!=4\\
x_{3} =3*3!=18\\
x_{4} =4*4!=96\\
S_{1} = x_{1}=1=2!-1\\
S_{2} = x_{1}+x_{2}=1+4=5=3!-1\\
S_{3} = x_{1}+x_{2}+x_{3}=5+18=23=4!-1\\
S_{4} = x_{1}+x_{2}+x_{3}+x_{4}=23+96=119=5!-1\\
\boxed{S_{n} = (n+1)!-1}\\
[/tex]
