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Math Help - [SOLVED] Root test question

  1. #1
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    [SOLVED] Root test question

    Would it be possible to determine if this series was convergent or divergent using the root test?



    Neither the top or the bottom are raised to the power of n so i've tried a number of things trying to work around it(taking the natural log, and L'Hosp rule) but it doesn't seem to be possible. Am I right that this can't be solved using the root test, or is there some way that I'm overlooking?
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by yzobel View Post
    Would it be possible to determine if this series was convergent or divergent using the root test?



    Neither the top or the bottom are raised to the power of n so i've tried a number of things trying to work around it(taking the natural log, and L'Hosp rule) but it doesn't seem to be possible. Am I right that this can't be solved using the root test, or is there some way that I'm overlooking?
    This is a non negative monotone decreasing function. Use integral test and you'll get the result

     \int_1^\infty \frac{n}{3+n^{2}} dn

    What do you get?
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by yzobel View Post
    Would it be possible to determine if this series was convergent or divergent using the root test?



    Neither the top or the bottom are raised to the power of n so i've tried a number of things trying to work around it(taking the natural log, and L'Hosp rule) but it doesn't seem to be possible. Am I right that this can't be solved using the root test, or is there some way that I'm overlooking?
    You are correct that the root test does not help try the integral test!
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