Factorials: Simplifying Expressions & Convergence Tests

[FancyNut]

I forgot most things about factorials but now I have to use them again to simplify expressions while doing convergence tests... What I know is:

$$(n +1) ! = (n +1) n!$$

$$(2n +1)! = (2n +1) 2n! ?$$

but I don't know how to deal with these:

$$(n -1) ! = ?$$

$$(2n-1) ! = ?$$

Thanks for any help.

 

[FancyNut]

I know they're pretty easy but I don't have any algebra text/reference to look them up...

 

[Yegor]

At first (2n+1)!=(2n)!(2n+1)
(n-1)!=n!/n
(2n-1)!=(2n)!/2n

 

[FancyNut]

Thank you, sir. :)