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Math Help - Power Series Representation Question Help

  1. #1
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    Power Series Representation Question Help

    Hi can someone please help me with the foloowing question. Thanks.

    Find a power series representation for the following functions:
    (a) f(x) =

    x^
    3/(3 + x^2)^2 :
    (b)


    f(x) = x^2 ln( cuberoot(2 + x^3)):
    (c)


    f(x) = 1/x about x0 = 3.


    Thank you to all who help in advance.

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by engineeringboy View Post
    Hi can someone please help me with the foloowing question. Thanks.

    Find a power series representation for the following functions:
    (a) f(x) =

    x^
    3/(3 + x^2)^2 :



    f(x)=\frac{x^3}{(3+x^2)^2}=\frac{x^3}{9} \times \frac{1}{(1+x^2/3)^2}

    Now expand the second part of the right hand side using the binomial expansion of 1/(1+u)^2 with u=x^2/3 then simplify.

    CB
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