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I need to find the limit of the following sequence

$x_n=\sqrt{n^2+1}-n$.

I am having trouble on where to start for this question. Any help would be appreciated.

Martin Sleziak
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Lily Lemont
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    Please tell us your efforts. – John B Jan 30 '16 at 02:08
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    You could start by looking at this other question from today, which is very similar. – Clement C. Jan 30 '16 at 02:15
  • Some related posts: http://math.stackexchange.com/questions/136495/calculate-lim-n-to-infty-sqrtn2n-n http://math.stackexchange.com/questions/408067/the-limit-lim-limits-n-to-infty-sqrtn2-n-n-algebraic-and-intuitive-t http://math.stackexchange.com/questions/587457/calculate-lim-n-to-infty-sqrtn2n-n http://math.stackexchange.com/questions/783536/prove-that-lim-sqrtn2n-n-frac12 http://math.stackexchange.com/questions/1632157/calculate-lim-n-to-infty-sqrtn2n-n – Martin Sleziak Jan 30 '16 at 04:18
  • Whenever a square root is involved, it is worth to consider multiplying with the conjugate –  Sep 24 '16 at 06:27

2 Answers2

2

Multiply the expression by $\frac{\sqrt{n^2+1}+n}{\sqrt{n^2+1}+n} $.

Nothing original here - move along now.

marty cohen
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1

Hint: Multiply and divide by $\sqrt{n^2+1} + n$

adjan
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