不知道對不對...好像不夠嚴謹
\( \displaystyle \sum_{1}^{\infty}\frac{1}{\sqrt{n}(n+1)}<\sum_{1}^{\infty}\frac{1}{n \sqrt{n}} \)⇒\( \int_{1}^{\infty}\frac{1}{x \sqrt{x}}dx=(-2 \times \frac{1}{\sqrt{x}})\bigm|_{1}^{\infty}=2 \)
∴\( \displaystyle \sum_{1}^{\infty} \frac{1}{\sqrt{n}(n+1)}<2 \)
