# Determining convergence of a collection

$\displaystyle\sum_{n=0}^{\infty}\sqrt{n}(\sqrt{n^4+1}-n^2)$

Ok I was actually reluctant to upload this due to the fact that it is such a primary inquiry, and also I actually need to have the ability to do this. Nonetheless, I've been considering this for over half a hr and also I've attempted several approaches, yet I'm unable to get the collection right into a wonderful kind where I can take the restriction. Any kind of suggestions on just how to tackle this trouble?

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2019-12-02 03:12:33
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Just keep in mind that $$\sqrt{n^4 + 1} - n^2 = \frac{( \sqrt{n^4 + 1} - n^2 )( \sqrt{n^4 + 1} + n^2 )}{\sqrt{n^4 + 1} + n^2} = \frac{n^4 + 1 - n^4}{\sqrt{n^4 + 1} + n^2} = \frac{1}{\sqrt{n^4 + 1} + n^2}$$ after that you can make use of the contrast examination.