11!-(1*1!+2*2!+3*3!+...+10*10!)= вычислить

Question

11!-(1*1!+2*2!+3*3!+...+10*10!)= вычислить

Answer 1

11!=11*10!

11!-(1*1!+2*2!+3*3!+...+10*10!)=11*10!-10*10!-(1*1!+...+9*9!)=
10!-(1*1!+...+9*9!)= 10*9!-9*9!-(1*1!+...+8*8!)=
9!-(1*1!+...+8*8!)= 
... 
3!-(1*1!+2*2!)=3*2!-2*2!-(1*1!)=
2!-(1*1!) = 2-1 = 1

Answer 2

11!=11*10!

11!-(1*1!+2*2!+3*3!+...+10*10!)=11*10!-10*10!-(1*1!+...+9*9!)=
10!-(1*1!+...+9*9!)= 10*9!-9*9!-(1*1!+...+8*8!)=
9!-(1*1!+...+8*8!)= 
... 
3!-(1*1!+2*2!)=3*2!-2*2!-(1*1!)=
2!-(1*1!) = 2-1 = 1