How to solve the sequence limit The sequence limit is: $$\lim_{n\to \infty}\left[\frac{\sqrt{n}-\sqrt{n-1}}{\sqrt{n+1}-\sqrt{n}}\right]$$ I rationalized and got: $$\lim_{n\to \infty}\left[\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n}-\sqrt{n-1}}\right]$$ After this procedure I got stuck

Hint. It should be $$\frac{\sqrt{n}-\sqrt{n-1}}{\sqrt{n+1}-\sqrt{n}}=\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n}+\sqrt{n-1}}=\frac{\sqrt{1+\frac{1}{n}}+1}{1+\sqrt{1-\frac{1}{n}}}.$$ Can you take it from here?