1!×3-2!×4+3!×5-4!×6+...+101!×103-102! =
= 1!×(1+2)-2!×(1+3)+3!×(1+4)-4!×(1+5)+...
...+101!×(1+102)-102! =
= 1!+2!-2!-3!+3!+4!-4!-5!+...
...+101!+102!-102! = 1! = 1
1!×3-2!×4+3!×5-4!×6+...+101!×103-102! =
= 1!×(1+2)-2!×(1+3)+3!×(1+4)-4!×(1+5)+...
...+101!×(1+102)-102! =
= 1!+2!-2!-3!+3!+4!-4!-5!+...
...+101!+102!-102! = 1! = 1