Calculating (n+2)! quickly and accurately - Help Needed!

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Homework Help Overview

The discussion revolves around calculating the factorial of (n+2) and understanding its relationship to n!. Participants are exploring how to express (n+2)! in terms of n! and discussing the implications of this relationship in a mathematical context.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to derive (n+2)! from the known expression for n! and are questioning how to accurately express this factorial in relation to n!. There are discussions about the terms involved in the factorial expansions and how they relate to each other.

Discussion Status

Some participants have provided guidance on how to expand (n+2)! and its relationship to n!. There is an ongoing exploration of the factorial expressions, and while some clarity has been offered, there is no explicit consensus on the final interpretation of the quotient.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the extent of direct solutions provided. The discussion includes assumptions about the understanding of factorial notation and operations.

Phyzwizz
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I know that n!=(1)(2)(3)...(n-1)(n)
I am confused how I can figure out what (n+2)! is in order to divide it by n!
How can I figure (n+2)! out and what is it, so that I won't have to ask if what I got is right.

Thanks!
 
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You have already written out the expansion for n!. Now, if you add 1 to n, what additional term must be included in n! to make it (n+1)! Once you figure this out, repeat to find
(n+2)!
 
3!=3*2*1
4!=4*3*2*1
10!=10*9*8*...*2*1
etc.
What is 10! divided by 8! then?
 
oh okay so (n+2)! would be (1)(2)(3)...(n-1)(n)(n+1)(n+2)?
 
Right. Now figure your quotient (n+2)!/n!.
 
Phyzwizz said:
oh okay so (n+2)! would be (1)(2)(3)...(n-1)(n)(n+1)(n+2)?
Which is the same as (n + 2)(n + 1) n!, right?
 
There is no n! in the quotient of (n+2)!/n!. Remember the expansion of (n+2)! is
(n+2)(n+1)n!. Dividing (n+2)! by n! is (n+2)(n+1)n!/n! = (n+2)(n+1).
 

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