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Math Help - find power series

  1. #1
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    find power series

    find the power series representation of the function.

    heres the equation: http://img260.imageshack.us/img260/9021/untitledph1.jpg

    need help.
    thanks.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    find the power series representation of the function.

    heres the equation: http://img260.imageshack.us/img260/9021/untitledph1.jpg

    need help.
    thanks.
    We know that, -1<x\leq 1
    \tan^{-1}x=x-\frac{x^3}{3}+\frac{x^5}{5}-...
    Know if you multiply this term by term for (1+x^2) we have,
    x-\frac{x^3}{3}+\frac{x^5}{5}-....+x^3-\frac{x^5}{3}+\frac{x^7}{5}-...
    x+\frac{2x^3}{3\cdot 1}-\frac{2x^5}{5\cdot 3}+\frac{2x^7}{7\cdot 5}-\frac{2x^9}{9\cdot 7}+...

    I just need to make the restriction,
    -1<x<1\, rather then the endpoint because the Cauchy product applies only for the interval of absolute convergence.
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