Question

Evaluate the factorial expression. (N+4)! N+4

Answer 1

`n \in \mathbb N\\\\ ((n+4)!)/(n+4)\\\\ =((n+3)! (n+4))/((n+4))\\\\ =(n+3)!`

Answer 2

The simplified form of given factorial expression is (N+3)!.

Explanation:

The given expression is

`((N+4)!)/(N+4)`

The n! is defined as

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

`n!=n(n-1)!`

The given expression can be written as

`((N+4)!)/(N+4)=((N+4)(N+4-1)!)/(N+4)`

`((N+4)!)/(N+4)=((N+4)(N+3)!)/(N+4)`

Cancel out the common factors.

`((N+4)!)/(N+4)=(N+3)!`

Therefore the simplified form of given factorial expression is (N+3)!.