№1.Вычислить.а)(8!-6!):330б) 15!/12!*3!№2.Сократить дробь. (n+1)!/n(n-2)!
а) (8!-6!)/330=(6!*7*8-6!)/330 = 6! * 55 / 330 = 6! / 6 = 5! = 1 * 2*3*4*5 = 120
б) 15! / (12! * 3!) = 12! * 13 * 14 * 15 / (12! * 3!) = 13*14*15 / 6 = 455
2. (n+1)! / n(n-2)! = (n-2)! * (n-1) * n (n+1) / n(n-2)! = (n-1)*(n+1) = n^2 -1
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а) (8!-6!)/330=(6!*7*8-6!)/330 = 6! * 55 / 330 = 6! / 6 = 5! = 1 * 2*3*4*5 = 120
б) 15! / (12! * 3!) = 12! * 13 * 14 * 15 / (12! * 3!) = 13*14*15 / 6 = 455
2. (n+1)! / n(n-2)! = (n-2)! * (n-1) * n (n+1) / n(n-2)! = (n-1)*(n+1) = n^2 -1