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Math Help - converges or diverges

  1. #1
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    converges or diverges

    <br />
\sum_1^{\infty} \frac{1}{\sqrt{{k^4}+3k}}<br />

    what test would u use for this? i'm thinking its prolly a telescoping series but i have no idea what to do.
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  2. #2
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    \frac{1}{{\sqrt {k^4  + 3k} }} < \frac{1}{{k^2 }}
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  3. #3
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    thats not true though...k^4 i < (k^4+3K)^1/2 .... does this prove divergance?
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  4. #4
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    Hello,

    k^4+3k>k^4

    \sqrt{k^4+3k}>\sqrt{k^4}=k^2 because f:x\mapsto \sqrt{x} is an increasing function.

    \frac{1}{\sqrt{k^4+3k}}<\frac{1}{k^2} because g:x\mapsto \frac{1}{x} is a decreasing function.


    And we know that \sum \frac{1}{k^a} converges if a>1
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