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Math Help - determine if it's converge

  1. #1
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    determine if it's converge

    \sum (ln k)^2/k

    use the root test or the ration test
    Last edited by wopashui; March 28th 2010 at 08:55 PM.
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    Try the integral test
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  3. #3
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    Quote Originally Posted by wopashui View Post
    \sum (ln k)^2/k

    use the root test or the ration test
    see attachment for solution:series converges
    Attached Thumbnails Attached Thumbnails determine if it's converge-sol.bmp  
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  4. #4
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    Quote Originally Posted by wopashui View Post
    \sum (ln k)^2/k

    use the root test or the ration test
    What values does k go between?

    Is it \sum_{k = 1}^{\infty}\frac{(\ln{k})^2}{k}?
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  5. #5
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    Quote Originally Posted by wopashui View Post
    \sum (ln k)^2/k

    use the root test or the ration test
    Before using blindly any "test", simply look at what the summand looks like. It is positive. The logarithm grows slowly to \infty, hence \frac{(\ln k)^2}{k} is a bit larger than \frac{1}{k}. But... wait! we know that \sum_k \frac{1}{k} diverges! So we just have to write \frac{(\ln k)^2}{k}\geq \frac{1}{k} when k\geq 3 to conclude: the series diverges.
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