Find a closed form expression for this sum:
1.1! + 2.2! + 3.3! + ... + n.n!
= 2.1! + 3.2! + 4.3! + ... + (n+1).n! - (1! + 2! + ... + n!)
= 2! + 3! + 4! + ... + (n+1)! - (1! + 2! + ... + n!)
= (n+1)! - 1