Register to reply 
Binomial expansion of a function with x raised to a power 
Share this thread: 
#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

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. 


#4
Oct713, 08:57 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682

Binomial expansion of a function with x raised to a power
Wait, wait don't tell me. I'm still working on it!



Register to reply 
Related Discussions  
Integral of e raised to a power (a function)  Calculus & Beyond Homework  13  
Power expansion of the Dirac Delta function?  Set Theory, Logic, Probability, Statistics  2  
How to do expansion as power series of any random function?  Advanced Physics Homework  1  
Power series expansion of a function of x  Calculus & Beyond Homework  2  
Limits of a function containing ln an raised to a power  Calculus & Beyond Homework  4 