calculus - Does $sumlimits_{n=1}^inftyfrac{1}{sqrt{n}+sqrt{n+1}}$ converge?

Does the following series converge or diverge?

$$\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$$
The methods I have at my disposal are geometric and harmonic series, comparison test, limit comparison test, and the ratio test.

Answer

It is not hard to see that

$$\sum_{n=1}^\infty\frac{1}{\sqrt{n+1}+\sqrt{n}}=\sum_{n=1}^\infty(\sqrt{n+1}-\sqrt{n})$$

As you know this series is divergent.