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Math Help - power series

  1. #1
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    Question power series

    The function f(x)= 2(x^2)arctan(x^10) is represented as a power series. What is the lowest term with a nonzero coeddicient.

    I cant seem to get the answer for this problem and any help is appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by [s]arah View Post
    The function f(x)= 2(x^2)arctan(x^10) is represented as a power series. What is the lowest term with a nonzero coeddicient.

    I cant seem to get the answer for this problem and any help is appreciated. Thanks.
    The power series at 0 for arctan is

    \tan^{-1}(x)=\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n+1}}{(2n+1)}

    so

    2x^2\tan^{-1}(x^{10})=2x^2\sum_{n=0}^{\infty}\frac{(-1)^n(x^{10})^{2n+1}}{(2n+1)}=2\sum_{n=0}^{\infty}\  frac{(-1)^nx^{20n+12}}{(2n+1)}

    From here just plug in n=0 to get the first term
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