1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Expanding (2n)!

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey all. Not super familiar with using factorials, however, they do pop up occasionally. I understand that n! = 1*2*3*...*n. How do we treat factorial when we are multiplying n by an integer before taking the factorial? I know the answer for expanding (2n)!, however, I do not see why. Thanks in advance.
     
  2. jcsd
  3. Mar 18, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    What don't you see? Think of this:

    4! = 4*3*2*1

    (2*4)! = 8! = 8*7*6*5*4*3*2*1
     
  4. Mar 18, 2013 #3
    so (2n)!=(2*1)*(4*3*2*1)*(6*5*4*3*2*1)*...*(2n*(2n-1)*...*1). This can be taken a step further, though correct?
     
  5. Mar 18, 2013 #4

    phinds

    User Avatar
    Gold Member
    2016 Award

    I don't think you get it. Look at post #2 again.
     
  6. Mar 18, 2013 #5
    (2n)!=(2n*(2n-1)*(2n-2)*...*1) ?
     
  7. Mar 18, 2013 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That's more like it!
     
  8. Mar 18, 2013 #7
    Okay. How exactly does that end up being: 1*2*3*...*n*(n+1)*(n+2)*(n+3)*...*(2n) ?
     
  9. Mar 18, 2013 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    How did (2*4)! = 8! end up being 1*2*3* ... *8? What are you not seeing?
     
  10. Mar 18, 2013 #9

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Look at counting to 2n this way:

    1,2,3,4,...,n-2,n-1,n - the sequence of all integers from 1 to n
    n+1,n+2,n+3,..., n+n-2,n+n-1,n+n - the sequence of integers from n+1 to 2n
     
  11. Mar 18, 2013 #10
    You've written it down correctly twice - one of them is in reverse order of the other. How can you not know that they are the same?

    1*2 = 2*1 etc
     
  12. Mar 18, 2013 #11
    For some reason I was having a hard time seeing from n+1 to 2n. I completely see it now. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Expanding (2n)!
  1. Solve (2n-1)! (Replies: 3)

  2. Expand polynomials (Replies: 6)

Loading...