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
2026-05-17 03:07:47.1778987267
How to solve the sequence limit
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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?