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Math Help - power series!

  1. #1
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    power series!

     \sum_{n=1}^{\infty} x^n

    pls i don't have any ideal of finding the sum-function of the above series, help.

    thanks
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  2. #2
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    Re: power series!

    Quote Originally Posted by lawochekel View Post
     \sum_{n=1}^{\infty} x^n

    find the sum-function of the above series
    Provided that |x|<1~\&~J\in\mathbb{Z} then  \sum_{n=J}^{\infty}{a x^n}=\frac{ax^J}{1-x} ~.
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  3. #3
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    Re: power series!

    Under the conditions given by Plato, this would be an infinite geometric series. You should read more about geometric sequences and series.
    Thanks from topsquark
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  4. #4
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    Re: power series!

     \sum_{n=1}^{\infty} x^n=x +  \sum_{n=2}^{\infty} x^n=x +  x\sum_{n=1}^{\infty} x^n

    we have the original sum again on the right hand side (multiplied by x). So

     \sum_{n=1}^{\infty} x^n=x +  x\sum_{n=1}^{\infty} x^n

    So

     (1-x)\sum_{n=1}^{\infty} x^n=x

    finally as others have said:

     \sum_{n=1}^{\infty} x^n=\frac{x}{1-x}
    Thanks from topsquark
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