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Math Help - Power Series Once Again

  1. #1
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    Power Series Once Again

    This stuff confuses me!!!

    Find the radius and the interval of convergence of the power series.

     \sum_{n=1}^{\infty} \frac{(x+1)^n}{n}
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    Quote Originally Posted by larson View Post
    This stuff confuses me!!!

    Find the radius and the interval of convergence of the power series.

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

    g(x) = \int f(x) \, dx= \sum_{n=1}^{\infty}\frac{(x+1)^{n}}{n}

    The ROC for f(x) is |x+1| < 1
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  3. #3
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    Quote Originally Posted by larson View Post
    This stuff confuses me!!!

    Find the radius and the interval of convergence of the power series.

     \sum_{n=1}^{\infty} \frac{(x+1)^n}{n}
    Quote Originally Posted by Isomorphism View Post
    f(x) = \sum_{n=1}^{\infty}(x+1)^{n-1}

    g(x) = \int f(x) \, dx= \sum_{n=1}^{\infty}\frac{(x+1)^{n}}{n}

    The ROC for f(x) is |x+1| < 1
    Or you could just apply the ratio test and force the limiting value to be less than 1 .....
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