# Coefficient of nth term in binomial series

• May 3rd 2011, 11:28 PM
mathguy80
Coefficient of nth term in binomial series
Hi Guys,

Another binomial expansion problem.

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

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

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

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

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

Thanks again for all your help!
• May 3rd 2011, 11:46 PM
FernandoRevilla
In general, for all $p\in\mathbb{R}$ :

$(1+x)^p=\displaystyle\sum_{n=0}^{+\infty}\binom{p} {n}x^n \quad (|x|<1)$
• May 4th 2011, 02:29 AM
mathguy80
Quote:

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

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

Thanks @FernandoRevilla. But how do I simplify this? 1/2! As far as I know factorials are for non-negative integers only?