
#1
Oct613, 12:26 PM

P: 123

Hey guys.
So I need to know how to Binomial expand the following function [itex]\frac{1}{(1x^{2})}[/itex]. I need this because I have to work out [itex]\prod^{∞}_{i=1}[/itex][itex]\frac{1}{(1x^{i})}[/itex] for i up to 6. But I have to do it with Binomial expansion. If i can learn how to do [itex]\frac{1}{(1x^{2})}[/itex] then the rest of the powers should be the same. I was under the impression that [itex]\frac{1}{(1x^{2})}[/itex] can be binomial expanded as [itex]1+(1)(x^{2})+(1)(2)\frac{(x^{2})^{2}}{2!}+(1)(2)(3)\frac{(x^{2})^{3}}{3!}+...[/itex] Is that correct? Thanks guys! 



#2
Oct613, 02:45 PM

P: 112




#3
Oct613, 03:51 PM

Mentor
P: 4,499

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. 



#4
Oct713, 08:57 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,886

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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