# Does ( 2(n+1))! = 2!(n+1)! ) ?

1. Jan 28, 2008

### Mattofix

1. The problem statement, all variables and given/known data

Just a quick on - this is a little bit out of a bigger question.

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

Do you know of anywhere on the net where i can find factorial properties?

Thanks

2. Jan 28, 2008

### scottie_000

No they are not equal.
If you write out those factorials explicitly you should see why
See http://en.wikipedia.org/wiki/Factorials" [Broken] if you want more info

Last edited by a moderator: May 3, 2017
3. Jan 28, 2008

### HallsofIvy

Staff Emeritus
Did you TRY anything at all? If n= 1, (2(n+1))!= (2(2))!= 4!= 24 while 2!(n+1)! = 2(2)= 4. You can't get simpler than that.

4. Jan 28, 2008

### Mattofix

yeah - i did after i posted - too hasty - sorry

5. Jan 29, 2008

### Mattofix

so im meant to calcultae the radius of convergence and i have got to

... lZl(2(n+1))!/(2n)!(n+1)^2

what shall i do with the (2(n+1))!/(2n)! ?

6. Jan 29, 2008

### HallsofIvy

Staff Emeritus
(2n)!= (2n)(2n-1)... (n+1)! so 2(n+1)!/(2n)!= 2/[(2n)(2n-1)...(n+2)!]. what happens to that as n goes to infinity?

7. Dec 29, 2009

### xsm113r

Re: Factorials

Hi, similar kind of question.

Find all solutions in positive integers a; b; c to the equation
a!b! = a! + b! + c!

I have rearranged and got (a!-1)(b!-1) = c!+1

And the only solutions I can find are a=3 b=3 c=4 but I can't be sure that they are the only ones. How would I go about finding other solutions?