Question

Evaluate the factorial expression (n-4)!/n+4

Answer 1

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

Step-by-step explanation:

The correct question is

Evaluate the factorial expression
`((n+4)!)/((n+4))`

we know that

The n! is defined as

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

so

`(n+4)!=(n+4)(n+4-1)!=(n+4)(n+3)!`

substitute in the given expression

`((n+4)(n+3)!)/((n+4))`

Simplify (n+4)

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

therefore

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

Answer 2

Evaluations shown below

Explanation:

Factorial of a Number

Given a non-negative integer number n, we define its factorial n! as the product of every integer from 1 to n in steps of 1. For example

5!=5*4*3*2*1=120

It's defined that 0!=1

We are required to evaluate the factorial expression (n-4)!/n+4. We are not given specific values of n, so we'll pick up some of them. Note that n-4 must be non-negative, so n must be greater or equal to 4.

For n=7

(7-4)!/7+4=3!/7+4=6/7+4=34/7

For n=8

(8-4)!/8+4=4!/8+4=24/8+4=7

For n=10

(10-4)!/10+4=6!/10+4=720/10+4=76