Product stuff

[Arrow_Raider]

I have a the following product:
3 * 5 * 7 * 9 * 11... where the number of elements is n. Basically, multiply the first n odd numbers, starting at 3.
I have written the situation using product notation, but I would like to know how to convert into something more usable. I already have the answer, but I don't know how to arrive at it.


The product and answer are above.

I also had a 2 * 4 * 6 * 8 * 10... situation that involved the even numbers instead. It was pretty clear how to take that out of the product notation.

[Shaggy Hiker]

I read your signature, thinking it was part of the question

Then I hit submit by mistake. I think I'm too tired to think, but I can't be sure.

What do you want to do with that? You talk about turning it into something useful, how do you mean?

[Arrow_Raider]

I have fixed a typo in the first image. It had said (n+1)! in numerator when it should have been (2n+1)!. Anyways, I see why it works; the numerator does 2*3*4*5*6*7*8*9... and then the bottom part of the fraction divides out the even numbers, leaving just the odd numbers. I hadn't noticed this before for some reason, but it would still be nice if I knew a way of arriving at this through some method or something.

[anhn]

At work, I cannot see the images in your post (blocked).
This is how the production of first n odd numbers starting from 3 converted to factorial and power of 2:

'                    1*2*3*4*5*6*7*...*(2n)*(2n+1)
' 3*5*7*...*(2n+1) = -----------------------------
'                          2*4*6*...*(2n)
'
'                         (2n+1)!       (2n+1)!
'                  = ---------------- = -------
'                    2n*(1*2*3*...*n)     2n*n!