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Homework Help: Binomial Theorem

  1. Oct 5, 2008 #1
    how do i use binomial to show that 3^k C(n,k) = 3^k 1^n-k C(n,k)
     
  2. jcsd
  3. Oct 5, 2008 #2

    CRGreathouse

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    Did you type that correctly? Right now you have stuff = stuff * 1, which is clearly correct...
     
  4. Oct 5, 2008 #3
    i wanted to explain a bit more
     
  5. Oct 5, 2008 #4
    It should be
    n
    sum 3^k C(n,k) = 2^2n
    k=0

    the hint is 3^k C(n,k) = 3^k 1^n-k C(n,k)
     
  6. Oct 10, 2008 #5

    HallsofIvy

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    The reason C(n, k) are called "binomial coefficients" is that C(n, k) is the coefficient of xk in (x+ y)n What are the coefficients of xk in (3x+ y)n? What do you get if x= y= 1?
     
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