1. Limited time only! Sign up for a free 30min personal 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!

Combination problem

  1. Dec 28, 2003 #1
    Can anyone explain to me why k!/(k!*(k-k)!)+(k+1)!/(k!*(k+1-k)!)+(k+2)!/(k!*(k+2-k)!)+...+(n-1)!/(k!*(n-1-k)!)=n!/((k+1)!*(n-k-1)!) please. Thanks a lot!
     
  2. jcsd
  3. Dec 29, 2003 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Look at the case where n = k+1... then the case where n = k+2...
     
  4. Dec 29, 2003 #3
    logarithm problem help

    can you help me with the four following problems by showing me the right procedures of doing it even though it's so troublesome? thanks alot and i would happily accept any recommended good sites from you guys for this topic.

    1)4(2^2x)=8(2^x)-4
    2)8(2^2x)-10(2^2x)+2
    3)3*2^2x-18(2^x)+24=0
    4)9^x-4(3^x)+3=0
     
  5. Dec 29, 2003 #4
    1)4(2^2x)=8(2^x)-4
    2)8(2^2x)-10(2^2x)+2
    3)3*2^2x-18(2^x)+24=0
    4)9^x-4(3^x)+3=0


    1) Substitute 2^x with t and the solve the quadratic equation

    2) Substitute 2^x with t and then solve the quadratic equation

    3) Substitute 2^x with t and the solve the quadratic equation

    4) Substitute 3^x with t and the solve the quadratic equation
     
  6. Dec 29, 2003 #5
    Hurkyl,

    Sorry, but I didn't quite get where you are going with n=k+1, etc. Could you please explain in more detail?
     
  7. Dec 29, 2003 #6

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    How about this:

    Assume that [tex]n-k > 1[/tex] and simplify:
    [tex]\frac{n!}{(k+1)!(n-k-1)!}-\frac{(n-1)!}{(k+1)!((n-1)-k-1)!}[/tex]

    Then compare it to the terms in your series.
     
  8. Dec 29, 2003 #7
    Now I see, thanks.
     
  9. Dec 29, 2003 #8
    I have just one more question:

    Why does n!/(0!*(n-0)!)+n!/(1!*(n-1)!)+...+n!/(n!*(n-n)!)=2^n ?
     
  10. Dec 30, 2003 #9

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Use the binomial theorem on [itex](1+1)^n[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook