急! F5數排列與組合q2

19.

n(n + 1)(n - 1)!
= (n + 1)(n)(n - 1)!
= (n + 1)(n)(n - 1)(n - 2)(n - 3)...(3)(2)(1)
= (n + 1)!

20.

n! + (n + 1)!
= n! + (n + 1)(n)!
= n!(1 + n + 1)
= n!(n + 2)

21.

(n - 2)! / n!
= (n - 2)! / [n(n - 1)(n - 2)!]
= 1 / [n(n - 1)]

22.

n(n - 1)! / [3!(n + 1)!]
= n! / [3!(n + 1)(n)!]
= 1 / [6(n + 1)]

23.

(n + 2)P(4)
= (n + 2)! / (n + 2 - 4)!
= (n + 2)! / (n - 2)!
= (n + 2)(n + 1)(n)(n - 1)(n - 2)! / (n - 2)!
= (n + 2)(n + 1)(n)(n - 1)

24.

(n - 1)P(3) / (n - 2)P(2)
= [(n - 1)(n)(n - 1)] / [(n - 2)(n - 1)]
= n(n - 1) / (n - 2)

25.

(n + 1)P(2) x (n - 1)P(2) - (n + 1)P(4)
= (n + 1)(n) x (n - 1)(n - 2) - (n + 1)(n)(n - 1)(n - 2)
= 0

26.

(n + 1)P(3) - (n - 1)P(3)
= (n + 1)(n)(n - 1) - (n - 1)(n - 2)(n - 3)
= (n - 1)[(n + 1)(n) - (n - 2)(n - 3)]
= (n - 1)(6n - 6)
= 6(n - 1)^2