# Develop a p series that represents a series

• Apr 5th 2007, 08:03 PM
thedoge
Develop a p series that represents a series
find a power series that reps 1/(1+x)^3 on the interval -1,1

now we know that 1/(1+x)= x^0-x^1+x^2-x^3+x^4-x^5+...

and I originally thought that I could cube each term to get

1/(1+x)^3=x^0-x^3+x^6-x^9+x^12-x^15+...

to get the p series = Sigma(n=0,infinity)[(-1)^n*x^(3n)]

but this I am not 100% sure of. Any tips?
• Apr 5th 2007, 08:32 PM
Jhevon
Quote:

Originally Posted by thedoge
find a power series that reps 1/(1+x)^3 on the interval -1,1

now we know that 1/(1+x)= x^0-x^1+x^2-x^3+x^4-x^5+...

and I originally thought that I could cube each term to get

1/(1+x)^3=x^0-x^3+x^6-x^9+x^12-x^15+...

to get the p series = Sigma(n=0,infinity)[(-1)^n*x^(3n)]

but this I am not 100% sure of. Any tips?

Ok, so i felt guilty about not being able to help you, so i looked some stuff up, and i came up with this. chances are there's a more efficient way to do it, since i'm still rusty on this stuff, but i'm pretty sure this is correct. hope you can see the image ok
• Apr 5th 2007, 11:13 PM
CaptainBlack
Quote:

Originally Posted by Jhevon
Ok, so i felt guilty about not being able to help you, so i looked some stuff up, and i came up with this. chances are there's a more efficient way to do it, since i'm still rusty on this stuff, but i'm pretty sure this is correct. hope you can see the image ok

Of course you could just use the binomial expansion of (1+x)^{-3}.

RonL
• Apr 6th 2007, 04:03 AM
thedoge
How would one accomplish solving it that way Captainblack?