# I Notation for Factorials!

1. Apr 27, 2016

### Staff: Mentor

I just have a quick question on how to write the notation for a factorial. I have a series with a factorial of 5*10*15*...*(5n) in it. Is this written as 5n!, as (5n)!, or something else? I'm pretty sure it's 5n!, as I've written 5n! out as 5(1*2*3*4*...*n), which when you distribute the 5 appears to come out as (5*10*15*...*5n), but I just wasn't sure if I'd broken some math rule somewhere.

Also, if it is 5n! and not (5n)!, can (5n)! be easily expressed in a form similar to (1*2*3*...*n)?

Thank you!

2. Apr 27, 2016

### axmls

Multiplication doesn't distribute over multiplication.

I think you're looking for a quintuple factorial, i.e. $(5n)!!!!!$. For instance, the double factorial is defined as $$(n)!!=n \cdot (n-2) \cdot (n-4) ... 1$$

3. Apr 27, 2016

### Staff: Mentor

Hah! Of course it doesn't! Silly me!
@phinds You're rubbing off on me, old man!

Thanks! I'll look into it!

4. Apr 28, 2016

### Staff: Mentor

This would be $5^n(1 * 2 * 3 * ... * n)$ or $5^n * n!$. Each of the n factors in the original expression has a factor of 5, which gives the $5^n$ part, and the remaining part is 1 * 2 * 3 * ... * n, or n!.

5. Apr 28, 2016

### Staff: Mentor

Gah! Somehow I missed the notification that you replied last night, Mark. I was just about to post the correct notation, which is 5nn!. Just got help from a tutor here on campus who figured it out. It all makes perfect sense now!

6. Apr 29, 2016

### ProfuselyQuarky

All these exclamation marks . . . everyone is so excited!!!!