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Math Help - Interval of Convergance

  1. #1
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    Interval of Convergance

    Find the interval of convergance of the series
    \sum_{n=1}^{\infty}\frac{3^n(x-2)^n}{\sqrt{n+2}*2^n}


    Can anyone walk me through slowly? I'm struggling a bit.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by kg7150 View Post
    Find the interval of convergance of the series
    \sum_{n=1}^{\infty}\frac{3^n(x-2)^n}{\sqrt{n+2}*2^n}


    Can anyone walk me through slowly? I'm struggling a bit.
    The \frac{1}{\sqrt{n+2}} is irrelevant. So, you are left with \left(\fac{3(x-2)}{2}\right)^n. This, is of course convergent iff \left|\frac{3(x-2)}{2}\right|<1.
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  3. #3
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    Thanks!

    I've gotten that far myself. Can you tell me about the convergence at the endpoints?

    Also *convergence
    Sorry about the spelling.
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by kg7150 View Post
    Thanks!

    I've gotten that far myself. Can you tell me about the convergence at the endpoints?

    Also *convergence
    Sorry about the spelling.
    \frac{1}{\sqrt{n+2}}>\frac{1}{n}
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