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Thread: Binomial theorem

  1. #1
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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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    The binomial theorem says that for $\displaystyle (x + y)^n$ the coefficient of $\displaystyle x^ky^{n-k}$ is $\displaystyle \binom{n}{k}$.

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

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