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Math Help - How to find a series expansion for x/(1-x) - Please help ASAP & thank you!

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    How to find a series expansion for x/(1-x) - Please help ASAP & thank you!

    I am confused on what this question means:

    Find a series expansion for the expression

    x/(1-x) for Abs(x)<1
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    Hello,

    \frac{x}{1-x}=x \cdot \frac{1}{1-x}=x \cdot \lim_{n \to \infty} \frac{1-x^n}{1-x}^{\color{red}*}=x \cdot \sum_{k=0}^\infty x^k=\dots



    {\color{red}*} \ : \ |x|<1, \lim_{n \to \infty} x^n=0
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    Quote Originally Posted by jgall View Post
    I am confused on what this question means:

    Find a series expansion for the expression

    x/(1-x) for Abs(x)<1
    That depends on where you are taking an expansion about.

    Typically this means a Maclaurin series for the function, that is to say a Taylor series about x = 0.

    -Dan
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