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!

Binomial Expansion Question Driving Me Mad

  1. Nov 9, 2006 #1
    Binomial Expansion Question Driving Me Mad!!!


    This is the last question on my maths sheet, and i must have been staring at it for hours, ive read all my notes and book but i just cant piece it together at all.

    Driving me crazy!

    You guys got any pointers, im really confused
  2. jcsd
  3. Nov 10, 2006 #2


    User Avatar

    a) (1 + x)^n = (n,0) + (n,1)x + ..... + (n,n)x^n
    (1 + x)^2n = (1 + x)^n(1 + x)^n
    Observe that x^n-2 * x^2 = x^n , the Hint shows that the coefficient (n,n-2) = (n,2) thus the coefficient of x^n will be (n,2)^2 and so forth for all powers of n. So it can be assumed that the coefficient of x^n = (n,0)^2 + (n,1)^2 + ..... + (n,n)^2.

    b) Obvious, by expansion. (1 + x)^2n = (2n, 0) + .... + (2n,n)x^n + ....+ (2n,2n)x^2n.

    c)By equating coefficients (2n,n) = (n,0)^2 + (n,1)^2 + .... + (n,n)^2
    The definition of (2n,n) = (2n)!/n!(2n-n)! = (2n)!/(n!)^2 as required.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Binomial Expansion Question Driving Me Mad
  1. Binomial expansion (Replies: 1)

  2. Binomial expansion (Replies: 7)