How Do You Approach This Limit Problem?

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\lim_{n\to infinity}{{(\sqrt{n^{2}+n+1}})-[{(\sqrt{n^{2}+n+1}})]} wer [.] is GIF
how will u solve this one
 
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For very large n, n^2 'dominates' lower powers so that is asymptotic to n- [n]. And that has no limit.
 

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