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Math Help - Binomial expansion

  1. #1
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    Binomial expansion

    From the binomial expansion theorem there are terms in
    x^{k+1}, x^ky, ...... , xy^k, y^{k+1}.
    What are the coefficients of the general term x^ry^{k+1-r} for:
    i) r = 0
    ii) r = 1,.....,k
    iii) r = k + 1
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by gtaplayr View Post
    From the binomial expansion theorem there are terms in
    x^{k+1}, x^ky, ...... , xy^k, y^{k+1}.
    What are the coefficients of the general term x^ry^{k+1-r} for:
    i) r = 0
    ii) r = 1,.....,k
    iii) r = k + 1
    See the Mathworld or the Wikipedia Article

    CB
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by gtaplayr View Post
    From the binomial expansion theorem there are terms in
    x^{k+1}, x^ky, ...... , xy^k, y^{k+1}.
    What are the coefficients of the general term x^ry^{k+1-r} for:
    i) r = 0
    ii) r = 1,.....,k
    iii) r = k + 1
    It seems you are using the definition: (x + y)^{k + 1} = \sum_{r = 0}^{k + 1} {k + 1 \choose r}x^ry^{k + 1 - r}.

    now just plug in the respective r's and you will be able to find the coefficients.
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