Question

Express n! using product notation.

Answer 1

Hello,


`n!=\prod_(i=1)^n{i}=1*2*3*4...*(n-1)*n`

Answer 2

The factorial of a positive integer
`n`, is the product of all positive integers less than or equal to
`n`. The factorial of
`n` is written as
`n!`.

By definition

`2!=2*1`

`3!=3*2*1`

`4!=4*3*2*1`

Therefore

`n!=n*(n-1)*(n-2)*(n-4)...*2*1`

This can rewritten as

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