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Math Help - Binomial Theorem Question

  1. #1
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    Binomial Theorem Question

    Use a binomial expansion to simplify:

    a) (10c0)+(10c1)3+(10c2)3^2+...+(10c10)3^10
    b) (nc0)-(nc1)+(nc2)-(nc3)+...+(-1)^n (ncn)

    c meaning chose

    Any help would be greatly appreciated, I seem to be struggling quite alot with this topic but hopefully after this question I will be professional.

    Thx in advance
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  2. #2
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    Quote Originally Posted by Solid8Snake View Post
    Use a binomial expansion to simplify:
    a) (10c0)+(10c1)3+(10c2)3^2+...+(10c10)3^10
    b) (nc0)-(nc1)+(nc2)-(nc3)+...+(-1)^n (ncn)
    You know \left( {1 + x} \right)^{10}  = \sum\limits_{k = 0}^{10} {\binom{10}{k}x^k } . Let x=3
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  3. #3
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    im not quite sure what you mean. Could you demonstrate with question a so that i get an idea how to apply to b.

    thx
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  4. #4
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    Do you understand this: \left( {y + x} \right)^{10}  = \sum\limits_{k = 0}^{10} {\binom{10}{k} y^{10-k}x^k } ?
    If not, I cannot help you.

    If you do understand that, then let y=1~\&~x=3.
    See if the right-hand side is exactly part a.
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  5. #5
    Member Greengoblin's Avatar
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    Just in case you're confused with the notation, {n\choose k}=^nC_k
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  6. #6
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    i understand most of what you posted Plato, however the only part i dont understand is the sigma sign (what does that represent because in school we never learnt that.)

    Thx again
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