# N /n! = ?

1. Jan 28, 2010

### S.N.

n!!/n! = ?

Hi, I have a quick question that's been bugging me: is there an easy simplification of (n!!)/(n!)? And how is is demonstrated?

2. Jan 28, 2010

### l'Hôpital

Re: n!!/n! = ?

Yup. Depends on whether n is even or odd.

Try working it out. The answer will come in terms of another double factorial.

EDIT: My bad, it does not depend on whether n is even or odd.

Last edited: Jan 28, 2010
3. Jan 28, 2010

### Norman.Galois

Re: n!!/n! = ?

I can hardly call it a simplication if it has another double factorial. I would just say it's another way to write it. It's equivalent.

The obvious answer to something that is equivalent...

(n!!-1)!

4. Jan 28, 2010

### l'Hôpital

Re: n!!/n! = ?

Why? We have a factorial and a double factorial and we can reduce it to just a double factorial.

That sounds like simplification to me.

5. Jan 29, 2010

### zgozvrm

Re: n!!/n! = ?

:rofl:
I laughed when I looked at your original question because I thought to myself:

$$\frac{n!!}{n!} = ?$$ ... that can't be; where does the "?" come from?

It should be $$\frac{n!!}{n!} = !$$ since the "n!" cancels out.

Like this: $$\frac{n!!}{n!} = \frac{(n!)!}{n!} = \frac{n!}{n!}\times ! = 1\times ! = !$$

6. Jan 29, 2010

### Norman.Galois

Re: n!!/n! = ?

In differential equations class, they had...

$$x = \frac{dy}{dx}$$

The student cancelled the d's, and then multiplied both sides by x and added "+C". That's $y = x^2 + C$. Argued his answer was correct and was only missing an insignificant coeficient and should get full marks.

7. Jan 29, 2010

### Phyisab****

Re: n!!/n! = ?

Im not a mathemagician. But you could use Stirling's approximation if you assume large n.

8. Jan 29, 2010

### Staff: Mentor

Re: n!!/n! = ?

That's like
$$\frac{sin x}{n}= 6$$

9. Jan 29, 2010

### zgozvrm

Re: n!!/n! = ?

Good one! (It took me a while, but I got it!)

10. Jan 29, 2010

### l'Hôpital

Re: n!!/n! = ?

I know a guy who actually did that on a Calculus Preparedness Exam for our physics class. Wherever there was d/dx, he would just cancel the d's and divide by x.

11. Jan 29, 2010

### Char. Limit

Re: n!!/n! = ?

Lol, it even kind of works for polynomials, if you commonly ignore coefficients...

12. Jan 29, 2010

### uart

Re: n!!/n! = ?

Actually it's $(n! - 1)!$. You slipped in an extra factorial there. :)

13. Jan 29, 2010

### Norman.Galois

Re: n!!/n! = ?

Hence why the student kept arguing.

14. Jan 29, 2010

### Char. Limit

Re: n!!/n! = ?

I would hardly call any coefficient insignificant, though.

What's the difference between $$x^3$$ and $$100x^3$$? Only an insignificant coefficient that changes the answer by a factor of 2.

15. Jan 29, 2010

### dacruick

Re: n!!/n! = ?

that is in the simplest possible form

16. Jan 29, 2010

### dacruick

Re: n!!/n! = ?

I mean, you have one variable and 3 of the same operators. What are you hoping for?

17. Jan 29, 2010

Re: n!!/n! = ?

n!!=n(n-2)(n-4).... right? I get 1/((n-1)!!) just by writing it out and cancelling out.

18. Jan 29, 2010

### l'Hôpital

Re: n!!/n! = ?

Good job. : )

19. Jan 29, 2010

### Norman.Galois

Re: n!!/n! = ?

OH!

I was thinking (n!)!.

20. Jan 30, 2010

### uart

Re: n!!/n! = ?

I thought the same thing here Norm. Maybe the OP could have explained it's meaning since it's not such a common symbol and easily confused.

Also I must say that I find "double factorial" a very unintuitive name for that function. It should be called "half factorial" IMHO.