Exercise 7, § 8 Algebra, I, 173 For all n∈N∗n \in \mathbf{N}^*n∈N∗, n!=∑ν=0n−1(−1)ν(nν)(n−ν)n n! = \sum_{\nu=0}^{n-1} (-1)^{\nu} \binom{n}{\nu} (n-\nu)^n n!=ν=0∑n−1(−1)ν(νn)(n−ν)n (use no. 2, Proposition 2). Solution No solution has been written yet.