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Math Help - radius of convergence

  1. #1
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    radius of convergence

    determine the radius of convergence and the interval of convergence of the power series as n goes from 1 to infinity of

    ((1-x)^2n) / ((4^n) * n)

    This was on a test and I missed it. Somehow I got negative infinity to infinity. I would like to see the proper steps. thanks in advance..
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by calculushelptx View Post
    determine the radius of convergence and the interval of convergence of the power series as n goes from 1 to infinity of

    ((1-x)^2n) / ((4^n) * n)

    This was on a test and I missed it. Somehow I got negative infinity to infinity. I would like to see the proper steps. thanks in advance..
    apply the root test. can you continue?
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  3. #3
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    I applied the ratio test and got 1/4 < 1 but cannot continue with root.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by calculushelptx View Post
    I applied the ratio test and got 1/4 < 1 but cannot continue with root.
    whatever you are applying, it is not the ratio test. by the ratio test, we get \bigg| \frac {(1 - x)^2}4\bigg|<1

    now find the range for x. and remember to check the endpoints when finished
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