# Thread: Coefficient of nth term in binomial series

1. ## Coefficient of nth term in binomial series

Hi Guys,

Another binomial expansion problem.

Write down the first 4 terms and the coefficient of $\displaystyle x^n$ in the expansions in ascending powers of x of the following expression.

$\displaystyle (1 - 2x)^{\frac{1}{2}}$

I got the first part, by expanding it as a binomial series,

$\displaystyle 1 - x - \frac{1}{2}x^2 - \frac{1}{2}x^3 + ...$

How do I find the coefficient of $\displaystyle x^n$? What kind of series are the coefficients in?

Thanks again for all your help!

2. In general, for all $\displaystyle p\in\mathbb{R}$ :

$\displaystyle (1+x)^p=\displaystyle\sum_{n=0}^{+\infty}\binom{p} {n}x^n \quad (|x|<1)$

3. Originally Posted by FernandoRevilla
In general, for all $\displaystyle p\in\mathbb{R}$ :

$\displaystyle (1+x)^p=\displaystyle\sum_{n=0}^{+\infty}\binom{p} {n}x^n \quad (|x|<1)$
Thanks @FernandoRevilla. But how do I simplify this? 1/2! As far as I know factorials are for non-negative integers only?