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Math Help - Integral Test 2

  1. #1
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    Integral Test 2

    \sum^{infinity}_{n=2} \frac {1}{n \sqrt{ln(n)}}

    I don't know how to use the integral test for this....
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  2. #2
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    Quote Originally Posted by saiyanmx89 View Post
    \sum^{infinity}_{n=2} \frac {1}{n \sqrt{ln(n)}}

    I don't know how to use the integral test for this....
    let u=\ln(x) \implies du=\frac{1}{x}dx so we get

    \int\frac{1}{x\sqrt{\ln(x)}}dx=\int \frac{1}{u^{\frac{1}{2}}}du
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  3. #3
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    so, it converges at 2 \sqrt{ln2} ???
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    Quote Originally Posted by saiyanmx89 View Post
    so, it converges at 2 \sqrt{ln2} ???

    Not quite the anti derivative is

    \lim_{b \to \infty} 2\sqrt{\ln(x)}\bigg|_{2}^{b}=\lim_{b \to \infty}2\sqrt{\ln(b)}-2\sqrt{\ln(2)}=\infty
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