How to sum factorials: $(n+1)! + n!$

Question

How can the sum of factorials $(n+1)!+n!$ be simplified?

Answer 1

HINT: $(n+1)! = (n+1)\cdot n!$. So... $$ (n+1)! + n! = (n+1)\cdot n! + n! = ... $$

Answer 2

$$(n+1)! = (n+1) \times n!$$

and so $$(n+1)! + n! = (n+1) \times n! + n!$$

and $$(n+1) \times n! + n! = n! ((n+1) +1) = n!(n+2)$$

and hence $$\color{blue}{(n+1)! +n! = n!(n+2)}$$