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Ofcourse I can see that $\lim_{n \to \infty} \sqrt{n+1}-\sqrt{n} = 0$ just by looking aat it, but how can I prove it in the right way?

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Hint: Use $a-b = \frac{a^2-b^2}{a+b}.$

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  • $\begingroup$ Why would anyone downvote this? Just for the laughs? $\endgroup$
    – Ennar
    Jan 3 '17 at 9:36
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hint: Use $0 < \sqrt{n+1} - \sqrt{n} < \dfrac{1}{\sqrt{n}}$

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