原式
=(2-1)x1!+2x2!+3x3!+4x4!+.+nxn!
=2!-1+2x2!+3x3!+4x4!+.+nxn!
=(1+2)x2!-1+3x3!+4x4!+.+nxn!
=3!-1+3x3!+4x4!+.+nxn!
=(1+3)x3!-1+4x4!+.+nxn!
=4!-1+5x5!+.+nxn!
.
=(n+1)!-1
原式
=(2-1)x1!+2x2!+3x3!+4x4!+.+nxn!
=2!-1+2x2!+3x3!+4x4!+.+nxn!
=(1+2)x2!-1+3x3!+4x4!+.+nxn!
=3!-1+3x3!+4x4!+.+nxn!
=(1+3)x3!-1+4x4!+.+nxn!
=4!-1+5x5!+.+nxn!
.
=(n+1)!-1