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Math Help - Develop a p series that represents a series

  1. #1
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    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?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by thedoge View Post
    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
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Jhevon View Post
    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
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  4. #4
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    How would one accomplish solving it that way Captainblack?
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