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Math Help - Comparison test and Limit Comparison test for series

  1. #1
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    Comparison test and Limit Comparison test for series

    Hi, I don't know how to show that the series Comparison test and Limit Comparison test for series-capture.png converges or diverges using the comparison test or limit comparison test. All the series so far have been rational.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by witcon View Post
    Hi, I don't know how to show that the series Click image for larger version. 

Name:	Capture.PNG 
Views:	26 
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ID:	19842 converges or diverges using the comparison test or limit comparison test. All the series so far have been rational.

    Thanks in advance.
    Note that \displaystyle \sqrt{n^4 + 1} - n^2 = \frac{1}{\sqrt{n^4 + 1} + n^2 }.
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  3. #3
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    What should I compare it with?
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  4. #4
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    \displaystyle \frac{1}{n^2}
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  5. #5
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    Quote Originally Posted by witcon View Post
    What should I compare it with?
    You are expected to note that \displaystyle \frac{1}{\sqrt{n^4 + 1} + n^2} < \frac{1}{\sqrt{n^4} + n^2} ....
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  6. #6
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    Which is also \displaystyle < \frac{1}{n^2}...
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