maduregimc

2021-12-26

What is the factorial of $(n+1)$ ?

zurilomk4

Beginner2021-12-27Added 35 answers

It is $n!\cdot (n+1)$

Explanation:

Since factorial n (or n!)) is the product of all numbers up to and including n, we only have to multiply by the next number.

Explanation:

Since factorial n (or n!)) is the product of all numbers up to and including n, we only have to multiply by the next number.

Virginia Palmer

Beginner2021-12-28Added 27 answers

As we know $n\ne n\times (n-1)!$

Put$n=n+1$ in above equation, hence

$(n+1)\ne (n+1)\times [(n+1)-1]!$

$(n+1)=(n\times 1)\times [n+1-1]!$

$(n+1)\ne (n+1)\times n$

Hence proved.

Put

Hence proved.

nick1337

Expert2022-01-08Added 573 answers

What is the factorial of n?

If n is some positive integer, then the factorial of n is the product of every natural number till n, or

And that way, the factorial of n+1 becomes

As you can clearly observe, the part of the second expansion till n is equal to the first expansion, the one for n factorial.

So,