Attachment 20311

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. (Worried)

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- Jan 3rd 2011, 05:02 AMcaramelcakeBinomial theorem
Attachment 20311

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. (Worried) - Jan 3rd 2011, 05:49 AMsnowtea
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 $\displaystyle n$. - Jan 4th 2011, 03:57 AMcaramelcake
finally understood it after so long! thanks :)