Thread: 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?

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

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

How would one accomplish solving it that way Captainblack?