# Binomial theorem

• Jan 3rd 2011, 05:02 AM
caramelcake
Binomial 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 AM
snowtea
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 AM
caramelcake
finally understood it after so long! thanks :)