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Math Help - power serie representation

  1. #1
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    power serie representation

    I 've got huge problem with one more example. Didi anyone know hoe to find power series representation of the function:


    f(x)= -4x/ (1+2(x)^2)^2


    Thank you all for all posible answeres
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  2. #2
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    Quote Originally Posted by mauro21pl View Post
    I 've got huge problem with one more example. Didi anyone know hoe to find power series representation of the function:


    f(x)= -4x/ (1+2(x)^2)^2


    Thank you all for all posible answeres
    What is the integral of f(x)?
    (Hint: it is an arctangent).

    Thus,
    INTEGRAL f(x) dx= -atan(4x)
    Now, express,
    -atan(4x)
    As an arctangent series.

    Afterwards take the derivative term-by-term.
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  3. #3
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    Quote Originally Posted by mauro21pl View Post
    I 've got huge problem with one more example. Didi anyone know hoe to find power series representation of the function:


    f(x)= -4x/ (1+2(x)^2)^2


    Thank you all for all posible answeres
    Use the binomial theorem on 1/(1+2(x)^2)^2:

    -4x/ (1+2(x)^2)^2=-4x{1+(-2)(2x^2)+(-2)(-3)/2! (2x^2)^2+...}

    .........................=sum(n=0, inf) (n+1) (-1)^(n+1) 2^(n+2) x^(2n+1)

    RonL
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