(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! :)

Re: (Factorials) How should I simplify this?

Never mind, I've figured it out now.

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

That equals $\displaystyle \left[n-1\right]$

Re: (Factorials) How should I simplify this?

Because $\displaystyle \frac{n!}{(n- 1)!}- \frac{n!}{n!}= \frac{n(n- 1)!}{(n- 1)!}- \frac{n!}{n!}= n- 1$