Simplifying Factorials: How to Simplify 2n+2!?

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Homework Help Overview

The discussion revolves around simplifying expressions involving factorials, specifically the expression 2n+2! and its interpretation. Participants are clarifying the correct notation and understanding of factorials in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the meaning of 2n+2! and whether it should be interpreted as (2n + 2)!. There is discussion about the differences between 2n! and (2n)!, as well as the importance of using parentheses for clarity.

Discussion Status

The discussion is ongoing, with participants providing corrections and clarifications regarding factorial notation. Some have noted the importance of proper notation to avoid confusion, and there is an acknowledgment of previous errors in writing the expression.

Contextual Notes

There is a focus on the correct interpretation of factorial expressions and the potential for misunderstanding due to notation. Participants are also reflecting on the need for clarity in mathematical writing.

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Just a quick question. I'm having problems with factorials. For example, how do you simplify 2n+2!? Is it 2n!*2n+1!?

Thanks everybody!
 
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Strictly speaking, 2n + 2! would be just 2n + 2, since 2! = 2. You probably meant (2n + 2)!, which is (2n + 2)*(2n + 1)*(2n)!.

Edit: added a missing factor in the above.


Note that 2n! is different from (2n)!. The first is 2(n*(n-1)*(n-2)*...*2*1). The second is 2n*(2n-1)*(2n-2)*...*2*1.

You should get into the habit of using parentheses...
 
Last edited:


Mark44 said:
You probably meant (2n + 2)!, which is (2n + 1)*(2n)!.
Actually, it's (2n+2)*(2n+1)*(2n)!, but I'm sure you knew that.
 


Yeah, knew that, but didn't manage to write it.
I edited my earlier post.
 

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