How to show that $\lim_{n \to \infty} \sqrt{n+1}-\sqrt{n} = 0$? [closed]

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?

• Apr 18 '17 at 3:39

Hint: Use $a-b = \frac{a^2-b^2}{a+b}.$
hint: Use $0 < \sqrt{n+1} - \sqrt{n} < \dfrac{1}{\sqrt{n}}$