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Pascal's Triangle and Binomial Theorem

  1. Oct 2, 2007 #1
    1. Evaluate the numbers for the coefficient of x4y9 in the expansion of (3x + y)13.

    2. The Binomial Theorem states that for every positive integer n,
    (x + y)n = C(n,0)xn + C(n,1)xn-1y + ... + C(n,n-1)xyn-1 + C(n,n)yn.

    3. I understand that the coefficients can be found from the n row of Pascal's triangle, where n = 13. Using the binomial theorem, my approach (which I'm not sure about) is:

    The coefficient is 3 * C(13,9) = 3 * 715 = 2145.

    Am I going about this correctly? Sorry if I didn't expand on the proof.

  2. jcsd
  3. Oct 2, 2007 #2


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    This is the 5th term from the end (if you start from x^13 then diminish x's power), so is C(13,9) consistent with the formula?

    And, you should have 34.
    Last edited: Oct 2, 2007
  4. Oct 2, 2007 #3
    I was just going to say, I forgot the exponent of x, so should be 34 * C(13,9).

    I used the exponent of y for the combination term, because I knew that

    C(13,9) = C(13,13-9) = C(13,4).


    34 * C(13,9) = 81 * 715 = 57,915.

    Is this better?
  5. Oct 3, 2007 #4


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    In the formula x^k is associated with C(n,k-1) isn't it?
  6. Oct 3, 2007 #5

    Thank you for helping me to better understand the relationships between the coefficients, exponents, and expressions in this area of discrete mathemetics!

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