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Math Help - Power Series

  1. #1
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    Power Series

    is there a closed-form for the following power series?
    \sum_{i = a}^{\infty} i \cdot x^{n \cdot i}

    p.s. i just know that
    1. \sum_{i = 0}^{\infty} x^{n \cdot i} = \frac{1}{1- x^n}
    2. \sum_{i = 0}^{\infty} i \cdot x^{i} = \frac{x}{(1-x)^2}

    Thanks
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  2. #2
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    Quote Originally Posted by graticcio View Post
    is there a closed-form for the following power series?
    \sum_{i = a}^{\infty} i \cdot x^{n \cdot i}

    p.s. i just know that
    1. \sum_{i = 0}^{\infty} x^{n \cdot i} = \frac{1}{1- x^n}
    2. \sum_{i = 0}^{\infty} i \cdot x^{i} = \frac{x}{(1-x)^2}

    Thanks
    Yes. Replace x with x^n in formula 2.
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