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I need to find simple limit: $$\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$$

I can't use L'Hôpital's rule, which I think is natural for such problems. How to calculate such limit using only basic methods (definition and simple transformations etc.)?

It's one problem (from 50 problems) I don't know how to solve from my homework.

Thanks for help.

3 Answers 3