Algebra problem ordinary numbers

[synkk]

http://www.wolframalpha.com/input/?i=(k+1)!(k+2)+-1

Could anyone explain how you get from (k+1)!(k+2) - 1 to (k+2)! - 1

step by step please, here is my attempts:

(k+1)k!(k+2) - 1
(k+1)(k+2)k! - 1
(k+1)(k+2)! -1
no idea where to go from here

 

[Mark44]

http://www.wolframalpha.com/input/?i=(k+1)!(k+2)+-1

Could anyone explain how you get from (k+1)!(k+2) - 1 to (k+2)! - 1

This is very straightforward. (k + 2)! = (k + 2)*(k + 1)!

step by step please, here is my attempts:

(k+1)k!(k+2) - 1
(k+1)(k+2)k! - 1
(k+1)(k+2)! -1
no idea where to go from here

 

[synkk]

This is very straightforward. (k + 2)! = (k + 2)*(k + 1)!

how? isn't (k+2)*(k+1)k!? how is that (k+2)!?

 

[Mark44]

how? isn't (k+2)*(k+1)k!?

Isn't (k+2)*(k+1)k! what?

how is that (k+2)!?

(k + 2)! = (k + 2)*(k + 1)! = (k + 2) * (k + 1) * k!

Let's look at ordinary numbers.

8! = 8 * 7! = 8 * 7 * 6!
= 8 * 7 * (6 * 5 * 4 * 3 * 2 * 1)
= 56 * 720 = 40320