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Math Help - convergent for the values ​​of x

  1. #1
    Member vernal's Avatar
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    convergent for the values ​​of x

    Hi,

    The following series is convergent for the values ​​of x?





    thanks
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  2. #2
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    Re: convergent for the values ​​of x

    Quote Originally Posted by vernal View Post
    Hi,

    The following series is convergent for the values ​​of x?





    thanks
    The ratio test states that the series will be convergent where \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| < 1 \end{align*}, divergent where \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| > 1 \end{align*}, and inconclusive where \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| = 1 \end{align*}. So a good place to start would be to evaluate where this ratio is less than 1.
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    Re: convergent for the values ​​of x

    Not necessary.
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    Re: convergent for the values ​​of x

    Quote Originally Posted by HallsofIvy View Post
    Not necessary.
    Seeing as your post was as useless as it was insulting, why not explain a quicker method for the OP?
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