# (Factorials) How should I simplify this?

• November 1st 2013, 03:29 PM
HABMD
(Factorials) How should I simplify this?
n![(1/n-1)! - (1/n!)]

The correct answer is apparently n-1, but I keep getting a different answer. This is what I did:

n![(n!-(n-1)!)/(n-1)!(n!)]
=n/(n-1)!

Could somebody please show me what I've done wrong or what I need to do differently? :) any help really appreciated! :)
• November 1st 2013, 03:42 PM
HABMD
Re: (Factorials) How should I simplify this?
Never mind, I've figured it out now.
• November 1st 2013, 03:48 PM
Plato
Re: (Factorials) How should I simplify this?
Quote:

Originally Posted by HABMD
n![(1/n-1)! - (1/n!)]
Could somebody please show me what I've done wrong or what I need to do differently?

I hope that you mean $n!\left[\frac{1}{(n-1)!}-\frac{1}{n!}\right]$. it is not what you wrote.

That equals $\left[n-1\right]$
• November 1st 2013, 05:40 PM
HallsofIvy
Re: (Factorials) How should I simplify this?
Because $\frac{n!}{(n- 1)!}- \frac{n!}{n!}= \frac{n(n- 1)!}{(n- 1)!}- \frac{n!}{n!}= n- 1$