Question

Question #d820e

Answer 1

By definition of factorial `(n+2)! =(n+2) * (n+1) * n * (n-1) * ... * 3 * 2 * 1`
Therefore
`((n+2)!)/2`
`color(white)("XXX")=((n+2) * (n+1) * n * (n-1) * ... * 3 * cancel2 *1)/cancel2`
`color(white)("XXX")=(n+2)(n+1)...3`

Answer 2

Divide the definition of factorial of `n+2` by 2.

Explanation:

From the definition of factorial `n!`, which is product of all integers from 1 to `n` included:

`1! =1`
`2! =1*2`
`3! =1*2*3`
`...`
`n! =1*2*...*(n-1)*n`

We have
`(n+2)! =1*2*...*(n+1)cdot(n+2)`

Dividing by 2 and omitting 1:

`((n+2)!)/2 =3*4*...*(n+1)cdot(n+2)`