How can I evaluate the infinite sum $\sum\_1^\infty \frac{1}{(n \sqrt{n+1} + (n+1)\sqrt{n})}$? I try to change that into the form $\sum\_1^\infty \frac{1}{(\sqrt{n} + \frac{n}{n+1}\sqrt{n+1})}-\frac{1}{(\sqrt{n+1} + \frac{n+1}{n}\sqrt{n})}$ and try to reduce the terms. But it seems not valid. I'm thinking of using some fourier transform techniques, any suggestions?