Question

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

Answer 1

$n \in \mathbb N\\\\ \frac{(n+4)!}{n+4}\\\\ =\frac{(n+3)! (n+4)}{(n+4)}\\\\ =(n+3)!$

Answer 2

Answer:

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

Step-by-step explanation:

The given expression is

$\frac{(N+4)!}{N+4}$

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

$\frac{(N+4)!}{N+4}=\frac{(N+4)(N+4-1)!}{N+4}$

$\frac{(N+4)!}{N+4}=\frac{(N+4)(N+3)!}{N+4}$

Cancel out the common factors.

$\frac{(N+4)!}{N+4}=(N+3)!$

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