Доказать, что
![(n^3-n)\,\,\, \vdots \,\,\,6](https://tex.z-dn.net/?f=%28n%5E3-n%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6)
Докажем методом мат. индукции
1) Базис индукции (n=1)
![(1^3-1)\,\,\, \vdots \,\,\,6\\ \\ 0\,\,\, \vdots \,\,\,6](https://tex.z-dn.net/?f=%281%5E3-1%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+0%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6)
Первое утверждение выполняется.
2) Предположим что и для n=k тоже выполняется
![(k^3-k)\,\,\, \vdots \,\,\,6](https://tex.z-dn.net/?f=%28k%5E3-k%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6)
3) Индукционный переход (n=k+1)
![((k+1)^3-(k+1))\,\,\, \vdots \,\,\,6\\ \\ (k+1)((k+1)^2-1)\,\,\, \vdots \,\,\,6\\ \\ (k+1)(k+1-1)(k+1+1)\,\,\, \vdots \,\,\,6\\ \\ k(k+1)(k+2)\,\,\, \vdots \,\,\,6\\ \\ (k^3+3k^2+2k)\,\,\, \vdots \,\,\,6\\ \\ (k^3-k+3k^2+3k)\,\,\, \vdots \,\,\,6\\ \\ \bigg(\underbrace{k^3-k}_\big{\vdots\,\,\,6}+\underbrace{3k(k+1)}_\big{\vdots\,\,\,\,6}\bigg)\,\,\, \vdots \,\,\,6](https://tex.z-dn.net/?f=%28%28k%2B1%29%5E3-%28k%2B1%29%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+%28k%2B1%29%28%28k%2B1%29%5E2-1%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+%28k%2B1%29%28k%2B1-1%29%28k%2B1%2B1%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+k%28k%2B1%29%28k%2B2%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+%28k%5E3%2B3k%5E2%2B2k%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+%28k%5E3-k%2B3k%5E2%2B3k%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6%5C%5C+%5C%5C+%5Cbigg%28%5Cunderbrace%7Bk%5E3-k%7D_%5Cbig%7B%5Cvdots%5C%2C%5C%2C%5C%2C6%7D%2B%5Cunderbrace%7B3k%28k%2B1%29%7D_%5Cbig%7B%5Cvdots%5C%2C%5C%2C%5C%2C%5C%2C6%7D%5Cbigg%29%5C%2C%5C%2C%5C%2C+%5Cvdots+%5C%2C%5C%2C%5C%2C6)
Доказать, что
![3k(k+1)](https://tex.z-dn.net/?f=3k%28k%2B1%29)
делится ли на 6 можно опять же мат индукцией
15 -7 = 8 гусей были серыми, а всего 15
значит, 8/15
10м 25 секунд в 1 минуте 60 сек 625/60= 10.25
Ответ:2,4464
Пошаговое объяснение: (23,42-54)×(-4,12+4,04)=2,4464