Question

lim n->бесконечности (√(n+1)-√n)
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Answer 1

$\lim_{n \to \infty} (\sqrt{n+1} -\sqrt{n} ) =  \lim_{n \to \infty} \frac{(\sqrt{n+1} -\sqrt{n})(\sqrt{n+1} +\sqrt{n})}{\sqrt{n+1} +\sqrt{n}} =\\\\= \lim_{n \to \infty} \frac{n+1-n}{\sqrt{n+1} +\sqrt{n}} =0$