Using the evaluation of the derangement numbers as given in

Using the evaluation of the derangement numbers as given in Theorem 6.3.1, provide a proof of the relation Dn = (n - 1)(Dn-2 + Dn-1), (n = 3,4,5,...). Theorem 6.3.1 For n > = 1, Dn = n!(1 - 1/1! + 1/2! - 1/3! + ?+ (-1)^n 1/n!).

Solution

https://drive.google.com/file/d/0B1CSVtsXrMv9MHRQcGxtcFZMMDQ/view?usp=sharing