If it says 2n! in my book, should I interpret that as (2n)! or 2(n!)?

Answer 1

I think that it should clarify what is meant.

Answer 2

This is a first! 8 answers, and they all are in agreement!

Answer 3

The common sense tells us that it should be 2(n!), i.e. 2 times n!.

Answer 4

Factorial only applies to the number it is next to, like powers.

So 2n! = 2 (n!) just like 2x⁷ = 2(x⁷)

Answer 5

It should strictly be interpreted as 2(n!) because the factorial takes precedence over the multiplication.

That being said, if you want to describe the exact problem and the context, perhaps with a picture, I could tell you whether they were being sloppy or not.

Answer 6

(2n)! 

= Γ(2 n + 1)

2(n!)

= 2 Γ(n + 1)

Answer 7

I would say, and this is backed by WolframAlpha,

2n! is considered to be 2*(n!)

Answer 8

If it doesn't have parenthesis anywhere, then only the n has the factorial:

2(n!)

The same logic goes with exponents:

2x²

The 2 is not squared, but here it is:

(2x)²

Answer 9

Based upon properties of operations, 2n! = 2 (n!)

Answer 10

2(n!).  If they meant (2n)!, then they should have described it as such.