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

Ответ:

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

Ответ #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

Источник: https://znanija.com/task/319790