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Math Help - Binomial theorem

  1. #1
    Junior Member
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    Binomial theorem

    Binomial theorem-wqor9cgxog3xowji8mzu.jpg

    I don't understand the basic concept of binomials and don't understand this question so I don't know where to begin. If anyone could give any pointers I'd really appreciate that a lot.
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  2. #2
    Senior Member
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    Dec 2010
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    The binomial theorem says that for (x + y)^n the coefficient of x^ky^{n-k} is \binom{n}{k}.

    (3 + 5x^2)(1 - \frac{1}{2x})^n
    Now, the second binomial expands into something like:
    (3 + 5x^2)(c_0 + c_1x^{-1} + ... + c_nx^{-n})
    Now, think about terms in the expansion:
    The constant term will be 3c_0 + 5x^2c_2x^{-2}
    The coefficient of x^{-1} is 3c_1x^{-1} + 5x^2c_3x^{-3}

    Use the binomial theorem to get values for c_1, c_2, ... that depend on n.
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  3. #3
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    finally understood it after so long! thanks
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