Math Help - Binomial Expansion

1. Binomial Expansion

Can someone remind me which Binomial Expansion formula is used to expand:

$\frac{1}{1+x^2} = 1 + (-1)x^2 + \frac{(-1)(-2)}{2!}(x^2)^2 + \frac{(-1)(-2)(-3)}{3!}(x^2)^3+...$

Thanks in advance.

2. Originally Posted by Air
Can someone remind me which Binomial Expansion formula is used to expand:

$\frac{1}{1+x^2} = 1 + (-1)x^2 + \frac{(-1)(-2)}{2!}(x^2)^2 + \frac{(-1)(-2)(-3)}{3!}(x^2)^3+...$

Thanks in advance.
You can do it much easier using the sum of an infinite geometric series formula:

$1 + r + r^2 + \, .... = \frac{1}{1 - r}$

(provided |r| < 1).

In your case $r = -x^2$.

3. If you really want to do it using the (generalized) binomial expansion, do it as $(a+ 1)^n$ with $a= x^2$ and n= -1.