Binomial Expansion

• Jan 10th 2009, 03:59 AM
Simplicity
Binomial Expansion
Can someone remind me which Binomial Expansion formula is used to expand:

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

• Jan 10th 2009, 04:43 AM
mr fantastic
Quote:

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

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

$1 + r + r^2 + \, .... = \frac{1}{1 - r}$
In your case $r = -x^2$.
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.