Question

Factorial of negative numbers is not defined.

• A. True
• B. False

Answer 1

The correct option is A True

As we know,
$5\times 4!=5!$
$\Rightarrow 4!=\frac{5!}{5}$
Similar derivations are depicted in the below table,
As per the above derivations,

$n!=\frac{(n+1)!}{(n+1)}$

Now, let's find the factorial of negative number say $(-1).$

$(-1)!=\frac{(-1+1)!}{(-1+1)}=\frac{0!}{0}=\frac{1}{0}(\because 0!=1)$

As we know, $\frac{\text{Anything}}{0}$ is not defined, thus $\frac{1}{0}$ is not defined.

As a result, the value of $(-1)!$ is not defined.

Therefore, option (a.) is the correct choice.