# Binomial expansion of a function with x raised to a power

by Dixanadu
Tags: binomial, expansion, function, power, raised
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 P: 123 Hey guys. So I need to know how to Binomial expand the following function $\frac{1}{(1-x^{2})}$. I need this because I have to work out $\prod^{∞}_{i=1}$$\frac{1}{(1-x^{i})}$ for i up to 6. But I have to do it with Binomial expansion. If i can learn how to do $\frac{1}{(1-x^{2})}$ then the rest of the powers should be the same. I was under the impression that $\frac{1}{(1-x^{2})}$ can be binomial expanded as $1+(-1)(-x^{2})+(-1)(-2)\frac{(-x^{2})^{2}}{2!}+(-1)(-2)(-3)\frac{(-x^{2})^{3}}{3!}+...$ Is that correct? Thanks guys!
 P: 112 Maybe this will help: http://en.wikipedia.org/wiki/Binomia...#Special_cases Good luck!
 Emeritus Sci Advisor PF Gold P: 4,500 This is correct, and you probably want to observe that (-1)/1! = -1 (-1)(-2)/2! = 1 (-1)(-2)(-3)/3! = -1 and you can probably guess the pattern as you continue.
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,346 Binomial expansion of a function with x raised to a power Wait, wait- don't tell me. I'm still working on it!

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