Step by step solution to "What is the factorial of (n+1) ?"

High School
Algebra
Pre-Algebra
Factors and multiples

maduregimc

Answered question

2021-12-26

What is the factorial of

(n + 1)

Answer & Explanation

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.

Virginia Palmer

Beginner2021-12-28Added 27 answers

As we know

n \neq n \times (n - 1)!

Put

n = n + 1

in above equation, hence

(n + 1) \neq (n + 1) \times [(n + 1) - 1]!

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

(n + 1) \neq (n + 1) \times n

Hence proved.

nick1337

Expert2022-01-08Added 777 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
$n! = 1 \cdot 2 \cdot 3 \cdot . . . \cdot n$
And that way, the factorial of n+1 becomes
$(n + 1)! = 1 \cdot 2 \cdot 3 \cdot . . . \cdot n \cdot (n + 1)$
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,
$(n + 1)! = n! \cdot (n + 1)$

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