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Math Help - indefinite integral, power series

  1. #1
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    indefinite integral, power series

    indefinite integral: (t/1-t^8) dt

    need to show this as a power series, and the radius of convergence.

    could use u sub i think.

    thanks for any help.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    indefinite integral: (t/1-t^8) dt

    need to show this as a power series, and the radius of convergence.

    could use u sub i think.

    thanks for any help.
    \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n, |x|<1.
    Therefore, \frac{1}{1-t^8} = \sum_{n=0}^{\infty} t^{8n}, |t| < 1.

    Thus, we get that \frac{t}{1-t^8} = \sum_{n=0}^{\infty} t^{8n+1}

    Can you now integrate term-by-term?
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