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Math Help - power series for 1/(1-x)^2

  1. #1
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    power series for 1/(1-x)^2

    so.. i know that the power series is \sum_{n=0}^\infty \ nx^{n-1}<br />
or  \sum_{n=0}^\infty \ (n+1)x^n

    what i'm not sure about is.. how to find the radius of convergence and the interval of convergence

    my book says that the radius of convergence is 1, but beyond that, i don't know how or why

    please help?
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  2. #2
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    Quote Originally Posted by buttonbear View Post
    so.. i know that the power series is \sum_{n=0}^\infty \ nx^{n-1}<br />
or  \sum_{n=0}^\infty \ (n+1)x^n

    what i'm not sure about is.. how to find the radius of convergence and the interval of convergence

    my book says that the radius of convergence is 1, but beyond that, i don't know how or why

    please help?
    use the ratio test to find the interval of convergence ...

    \lim_{n \to \infty} \left|\frac{(n+2)x^{n+1}}{(n+1)x^n}\right| < 1

    |x| \lim_{n \to \infty} \frac{n+2}{n+1} < 1

    |x| \cdot 1 < 1

    -1 < x < 1
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